nn/chapter13.ipynb

{
 "cells": [
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "### 前面的13.1 13.2 因为不可抗力事件消失了（保存的时候乱码了）",
   "id": "b23af7657da5adfb"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:47:55.425519349Z",
     "start_time": "2026-07-27T09:47:53.873571522Z"
    }
   },
   "cell_type": "code",
   "source": [
    "\n",
    "import torch\n",
    "from d2l import torch as d2l"
   ],
   "id": "b39ef644f6c80c7c",
   "outputs": [],
   "execution_count": 1
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:47:55.671442114Z",
     "start_time": "2026-07-27T09:47:55.428215388Z"
    }
   },
   "cell_type": "code",
   "source": [
    "d2l.set_figsize()\n",
    "img = d2l.plt.imread('../data/catdog.jpg')\n",
    "d2l.plt.imshow(img);"
   ],
   "id": "4284e525ebcc7e87",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 350x250 with 1 Axes>"
      ],
      "image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"220.346324pt\" height=\"173.353814pt\" viewBox=\"0 0 220.346324 173.353814\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n <metadata>\n  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n   <cc:Work>\n    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n    <dc:date>2026-07-27T17:47:55.619678</dc:date>\n    <dc:format>image/svg+xml</dc:format>\n    <dc:creator>\n     <cc:Agent>\n      <dc:title>Matplotlib v3.7.2, https://matplotlib.org/</dc:title>\n     </cc:Agent>\n    </dc:creator>\n   </cc:Work>\n  </rdf:RDF>\n </metadata>\n <defs>\n  <style type=\"text/css\">*{stroke-linejoin: round; stroke-linecap: butt}</style>\n </defs>\n <g id=\"figure_1\">\n  <g id=\"patch_1\">\n   <path d=\"M 0 173.353814 \nL 220.346324 173.353814 \nL 220.346324 0 \nL 0 0 \nz\n\"/>\n  </g>\n  <g id=\"axes_1\">\n   <g id=\"patch_2\">\n    <path d=\"M 33.2875 149.475689 \nL 213.146324 149.475689 \nL 213.146324 10.875689 \nL 33.2875 10.875689 \nz\n\"/>\n   </g>\n   <g clip-path=\"url(#p5074bdf23f)\">\n    <image xlink:href=\"data:image/png;base64,\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
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 2
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:47:55.747558006Z",
     "start_time": "2026-07-27T09:47:55.673122195Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def box_corner_to_center(boxes):\n",
    "    \"\"\"从（左上，右下）转换到（中间，宽度，高度）\"\"\"\n",
    "    x1, y1, x2, y2 = boxes[:, 0], boxes[:, 1], boxes[:, 2], boxes[:, 3]\n",
    "    cx = (x1 + x2) / 2\n",
    "    cy = (y1 + y2) / 2\n",
    "    w = x2 - x1\n",
    "    h = y2 - y1\n",
    "    boxes = torch.stack((cx, cy, w, h), axis=-1)\n",
    "    return boxes\n",
    "def box_center_to_corner(boxes):\n",
    "    \"\"\"从（中间，宽度，高度）转换到（左上，右下）\"\"\"\n",
    "    cx, cy, w, h = boxes[:, 0], boxes[:, 1], boxes[:, 2], boxes[:, 3]\n",
    "    x1 = cx - 0.5 * w\n",
    "    y1 = cy - 0.5 * h\n",
    "    x2 = cx + 0.5 * w\n",
    "    y2 = cy + 0.5 * h\n",
    "    boxes = torch.stack((x1, y1, x2, y2), axis=-1)\n",
    "    return boxes"
   ],
   "id": "ee53061c33ad70d7",
   "outputs": [],
   "execution_count": 3
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:47:55.853579240Z",
     "start_time": "2026-07-27T09:47:55.749428064Z"
    }
   },
   "cell_type": "code",
   "source": "dog_bbox, cat_bbox = [60.0, 45.0, 378.0, 516.0], [400.0, 112.0, 655.0, 493.0]",
   "id": "2e45aa7592a4d7b1",
   "outputs": [],
   "execution_count": 4
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:47:55.959910400Z",
     "start_time": "2026-07-27T09:47:55.859086964Z"
    }
   },
   "cell_type": "code",
   "source": [
    "boxes = torch.tensor((dog_bbox, cat_bbox))\n",
    "box_center_to_corner(box_corner_to_center(boxes)) == boxes"
   ],
   "id": "22f2ce93eb46eca2",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[True, True, True, True],\n",
       "        [True, True, True, True]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 5
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:47:57.527570250Z",
     "start_time": "2026-07-27T09:47:57.492961332Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def bbox_to_rect(bbox, color):\n",
    "    # 将边界框(左上x,左上y,右下x,右下y)格式转换成matplotlib格式：\n",
    "    # ((左上x,左上y),宽,高)\n",
    "    return d2l.plt.Rectangle(\n",
    "    xy=(bbox[0], bbox[1]), width=bbox[2]-bbox[0], height=bbox[3]-bbox[1],\n",
    "    fill=False, edgecolor=color, linewidth=2)"
   ],
   "id": "cc21e1e13103291",
   "outputs": [],
   "execution_count": 6
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:47:57.635071582Z",
     "start_time": "2026-07-27T09:47:57.528293612Z"
    }
   },
   "cell_type": "code",
   "source": [
    "fig = d2l.plt.imshow(img)\n",
    "fig.axes.add_patch(bbox_to_rect(dog_bbox, 'blue'))\n",
    "fig.axes.add_patch(bbox_to_rect(cat_bbox, 'red'))"
   ],
   "id": "a4f3af406f8b5b1c",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.patches.Rectangle at 0x7f64a187bf90>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 350x250 with 1 Axes>"
      ],
      "image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"220.346324pt\" height=\"173.353814pt\" viewBox=\"0 0 220.346324 173.353814\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n <metadata>\n  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n   <cc:Work>\n    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n    <dc:date>2026-07-27T17:47:57.594042</dc:date>\n    <dc:format>image/svg+xml</dc:format>\n    <dc:creator>\n     <cc:Agent>\n      <dc:title>Matplotlib v3.7.2, https://matplotlib.org/</dc:title>\n     </cc:Agent>\n    </dc:creator>\n   </cc:Work>\n  </rdf:RDF>\n </metadata>\n <defs>\n  <style type=\"text/css\">*{stroke-linejoin: round; stroke-linecap: butt}</style>\n </defs>\n <g id=\"figure_1\">\n  <g id=\"patch_1\">\n   <path d=\"M 0 173.353814 \nL 220.346324 173.353814 \nL 220.346324 0 \nL 0 0 \nz\n\"/>\n  </g>\n  <g id=\"axes_1\">\n   <g id=\"patch_2\">\n    <path d=\"M 33.2875 149.475689 \nL 213.146324 149.475689 \nL 213.146324 10.875689 \nL 33.2875 10.875689 \nz\n\"/>\n   </g>\n   <g clip-path=\"url(#p30492a3230)\">\n    <image xlink:href=\"data:image/png;base64,\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
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 7
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:47:57.702782485Z",
     "start_time": "2026-07-27T09:47:57.650116830Z"
    }
   },
   "cell_type": "code",
   "source": [
    "#@save\n",
    "def multibox_prior(data, sizes, ratios):\n",
    "    \"\"\"生成以每个像素为中心具有不同形状的锚框\"\"\"\n",
    "    in_height, in_width = data.shape[-2:]\n",
    "    device, num_sizes, num_ratios = data.device, len(sizes), len(ratios)\n",
    "    boxes_per_pixel = (num_sizes + num_ratios - 1)\n",
    "    size_tensor = torch.tensor(sizes, device=device)\n",
    "    ratio_tensor = torch.tensor(ratios, device=device)\n",
    "\n",
    "    # 为了将锚点移动到像素的中心，需要设置偏移量。\n",
    "    # 因为一个像素的高为1且宽为1，我们选择偏移我们的中心0.5\n",
    "    offset_h, offset_w = 0.5, 0.5\n",
    "    steps_h = 1.0 / in_height  # 在y轴上缩放步长\n",
    "    steps_w = 1.0 / in_width   # 在x轴上缩放步长\n",
    "\n",
    "    # 生成锚框的所有中心点\n",
    "    center_h = (torch.arange(in_height, device=device) + offset_h) * steps_h\n",
    "    center_w = (torch.arange(in_width, device=device) + offset_w) * steps_w\n",
    "    shift_y, shift_x = torch.meshgrid(center_h, center_w, indexing='ij')\n",
    "    shift_y, shift_x = shift_y.reshape(-1), shift_x.reshape(-1)\n",
    "\n",
    "    # 生成 “boxes_per_pixel” 个高和宽，\n",
    "    # 之后用于创建锚框的四角坐标(xmin,xmax,ymin,ymax)\n",
    "    w = torch.cat((size_tensor * torch.sqrt(ratio_tensor[0]),\n",
    "                   sizes[0] * torch.sqrt(ratio_tensor[1:])))\\\n",
    "        * in_height / in_width  # 处理矩形输入\n",
    "\n",
    "    h = torch.cat((size_tensor / torch.sqrt(ratio_tensor[0]),\n",
    "                   sizes[0] / torch.sqrt(ratio_tensor[1:])))\n",
    "\n",
    "    # 除以2来获得半高和半宽\n",
    "    anchor_manipulations = torch.stack((-w, -h, w, h)).T.repeat(\n",
    "        in_height * in_width, 1) / 2\n",
    "\n",
    "    # 每个中心点都将有 “boxes_per_pixel” 个锚框，\n",
    "    # 所以生成含所有锚框中心的网格，重复了 “boxes_per_pixel” 次\n",
    "    out_grid = torch.stack([shift_x, shift_y, shift_x, shift_y],\n",
    "                           dim=1).repeat_interleave(boxes_per_pixel, dim=0)\n",
    "    output = out_grid + anchor_manipulations\n",
    "    return output.unsqueeze(0)"
   ],
   "id": "874f386629d410fb",
   "outputs": [],
   "execution_count": 8
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:47:57.754193331Z",
     "start_time": "2026-07-27T09:47:57.704574735Z"
    }
   },
   "cell_type": "code",
   "source": [
    "img = d2l.plt.imread('../data/catdog.jpg')\n",
    "h, w = img.shape[:2]"
   ],
   "id": "df3d1ba4aeb6c2f7",
   "outputs": [],
   "execution_count": 9
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:47:57.820044630Z",
     "start_time": "2026-07-27T09:47:57.755572144Z"
    }
   },
   "cell_type": "code",
   "source": [
    "print(h, w)\n",
    "X = torch.rand(size=(1, 3, h, w))\n",
    "Y = multibox_prior(X, sizes=[0.75, 0.5, 0.25], ratios=[1, 2, 0.5])\n",
    "Y.shape"
   ],
   "id": "e8737b3210446831",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "561 728\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "torch.Size([1, 2042040, 4])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 10
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:47:57.877041771Z",
     "start_time": "2026-07-27T09:47:57.821962159Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def show_bboxes(axes, bboxes, labels=None, colors=None):\n",
    "    \"\"\"显示所有边界框\"\"\"\n",
    "    def _make_list(obj, default_values=None):\n",
    "        if obj is None:\n",
    "            obj = default_values\n",
    "        elif not isinstance(obj, (list, tuple)):\n",
    "            obj = [obj]\n",
    "        return obj\n",
    "\n",
    "    labels = _make_list(labels)\n",
    "    colors = _make_list(colors, ['b', 'g', 'r', 'm', 'c'])\n",
    "    for i, bbox in enumerate(bboxes):\n",
    "        color = colors[i % len(colors)]\n",
    "        rect = d2l.bbox_to_rect(bbox.detach().numpy(), color)\n",
    "        axes.add_patch(rect)\n",
    "        if labels and len(labels) > i:\n",
    "            text_color = 'k' if color == 'w' else 'w'\n",
    "            axes.text(rect.xy[0], rect.xy[1], labels[i],\n",
    "                      va='center', ha='center', fontsize=9, color=text_color,\n",
    "                      bbox=dict(facecolor=color, lw=0))"
   ],
   "id": "e7070cbdb1d68616",
   "outputs": [],
   "execution_count": 11
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:47:57.924927279Z",
     "start_time": "2026-07-27T09:47:57.877778001Z"
    }
   },
   "cell_type": "code",
   "source": "boxes = Y.reshape(h, w, 5, 4)",
   "id": "4cc20a550931aef7",
   "outputs": [],
   "execution_count": 12
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:47:58.080082507Z",
     "start_time": "2026-07-27T09:47:57.926102351Z"
    }
   },
   "cell_type": "code",
   "source": [
    "bbox_scale = torch.tensor((w, h, w, h))\n",
    "fig = d2l.plt.imshow(img)\n",
    "show_bboxes(fig.axes, boxes[250, 250, :, :] * bbox_scale,\n",
    "    ['s=0.75, r=1', 's=0.5, r=1', 's=0.25, r=1', 's=0.75, r=2',\n",
    "        's=0.75, r=0.5'])"
   ],
   "id": "2daf2903aa5b1516",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 350x250 with 1 Axes>"
      ],
      "image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"233.229634pt\" height=\"185.525265pt\" viewBox=\"0 0 233.229634 185.525265\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n <metadata>\n  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n   <cc:Work>\n    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n    <dc:date>2026-07-27T17:47:58.021417</dc:date>\n    <dc:format>image/svg+xml</dc:format>\n    <dc:creator>\n     <cc:Agent>\n      <dc:title>Matplotlib v3.7.2, https://matplotlib.org/</dc:title>\n     </cc:Agent>\n    </dc:creator>\n   </cc:Work>\n  </rdf:RDF>\n </metadata>\n <defs>\n  <style type=\"text/css\">*{stroke-linejoin: round; stroke-linecap: butt}</style>\n </defs>\n <g id=\"figure_1\">\n  <g id=\"patch_1\">\n   <path d=\"M -0 185.525265 \nL 233.229634 185.525265 \nL 233.229634 0 \nL -0 0 \nz\n\"/>\n  </g>\n  <g id=\"axes_1\">\n   <g id=\"patch_2\">\n    <path d=\"M 46.170811 161.64714 \nL 226.029634 161.64714 \nL 226.029634 23.04714 \nL 46.170811 23.04714 \nz\n\"/>\n   </g>\n   <g clip-path=\"url(#p81be786314)\">\n    <image xlink:href=\"data:image/png;base64,\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
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 13
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:47:58.134645045Z",
     "start_time": "2026-07-27T09:47:58.116726506Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def box_iou(boxes1, boxes2):\n",
    "    \"\"\"计算两个锚框或边界框列表中成对的交并比\"\"\"\n",
    "    box_area = lambda boxes: ((boxes[:, 2] - boxes[:, 0]) *\n",
    "    (boxes[:, 3] - boxes[:, 1]))\n",
    "    # boxes1,boxes2,areas1,areas2的形状:\n",
    "    # boxes1：(boxes1的数量,4),\n",
    "    # boxes2：(boxes2的数量,4),\n",
    "    # areas1：(boxes1的数量,),\n",
    "    # areas2：(boxes2的数量,)\n",
    "    areas1 = box_area(boxes1)\n",
    "    areas2 = box_area(boxes2)\n",
    "    # inter_upperlefts,inter_lowerrights,inters的形状:\n",
    "    # (boxes1的数量,boxes2的数量,2)\n",
    "    inter_upperlefts = torch.max(boxes1[:, None, :2], boxes2[:, :2])\n",
    "    inter_lowerrights = torch.min(boxes1[:, None, 2:], boxes2[:, 2:])\n",
    "    inters = (inter_lowerrights - inter_upperlefts).clamp(min=0)\n",
    "    # inter_areasandunion_areas的形状:(boxes1的数量,boxes2的数量)\n",
    "    inter_areas = inters[:, :, 0] * inters[:, :, 1]\n",
    "    union_areas = areas1[:, None] + areas2 - inter_areas\n",
    "    return inter_areas / union_areas"
   ],
   "id": "ffe3178858e5a9b1",
   "outputs": [],
   "execution_count": 14
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:47:58.193234091Z",
     "start_time": "2026-07-27T09:47:58.136182636Z"
    }
   },
   "cell_type": "code",
   "source": [
    "#@save\n",
    "def assign_anchor_to_bbox(ground_truth, anchors, device, iou_threshold=0.5):\n",
    "    \"\"\"将最接近的真实边界框分配给锚框\"\"\"\n",
    "    num_anchors, num_gt_boxes = anchors.shape[0], ground_truth.shape[0]\n",
    "    # 位于第i行和第j列的元素x_ij是锚框i和真实边界框j的IoU\n",
    "    jaccard = box_iou(anchors, ground_truth)\n",
    "    # 对于每个锚框，分配的真实边界框的张量\n",
    "    anchors_bbox_map = torch.full((num_anchors,), -1, dtype=torch.long,\n",
    "    device=device)\n",
    "    # 根据阈值，决定是否分配真实边界框\n",
    "    max_ious, indices = torch.max(jaccard, dim=1)\n",
    "    anc_i = torch.nonzero(max_ious >= iou_threshold).reshape(-1)\n",
    "    box_j = indices[max_ious >= iou_threshold]\n",
    "    anchors_bbox_map[anc_i] = box_j\n",
    "    col_discard = torch.full((num_anchors,), -1)\n",
    "    row_discard = torch.full((num_gt_boxes,), -1)\n",
    "    for _ in range(num_gt_boxes):\n",
    "        max_idx = torch.argmax(jaccard)\n",
    "        box_idx = (max_idx % num_gt_boxes).long()\n",
    "        anc_idx = (max_idx / num_gt_boxes).long()\n",
    "        anchors_bbox_map[anc_idx] = box_idx\n",
    "        jaccard[:, box_idx] = col_discard\n",
    "        jaccard[anc_idx, :] = row_discard\n",
    "    return anchors_bbox_map\n"
   ],
   "id": "2ebf82c1768e24c6",
   "outputs": [],
   "execution_count": 15
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:47:58.260217572Z",
     "start_time": "2026-07-27T09:47:58.212670597Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def offset_boxes(anchors, assigned_bb, eps=1e-6):\n",
    "    \"\"\"对锚框偏移量的转换\"\"\"\n",
    "    c_anc = d2l.box_corner_to_center(anchors)\n",
    "    c_assigned_bb = d2l.box_corner_to_center(assigned_bb)\n",
    "    offset_xy = 10 * (c_assigned_bb[:, :2] - c_anc[:, :2]) / c_anc[:, 2:]\n",
    "    offset_wh = 5 * torch.log(eps + c_assigned_bb[:, 2:] / c_anc[:, 2:])\n",
    "    offset = torch.cat([offset_xy, offset_wh], axis=1)\n",
    "    return offset"
   ],
   "id": "b83220e939515b39",
   "outputs": [],
   "execution_count": 16
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:47:58.309313551Z",
     "start_time": "2026-07-27T09:47:58.261240696Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def multibox_target(anchors, labels):\n",
    "    \"\"\"使用真实边界框标记锚框\"\"\"\n",
    "    batch_size, anchors = labels.shape[0], anchors.squeeze(0)  # 问题：这里赋值给 anchors 会覆盖，但原代码就是这样\n",
    "    batch_offset, batch_mask, batch_class_labels = [], [], []\n",
    "    device, num_anchors = anchors.device, anchors.shape[0]\n",
    "    for i in range(batch_size):\n",
    "        label = labels[i, :, :]\n",
    "        anchors_bbox_map = assign_anchor_to_bbox(\n",
    "            label[:, 1:], anchors, device)\n",
    "        bbox_mask = ((anchors_bbox_map >= 0).float().unsqueeze(-1)).repeat(\n",
    "            1, 4)\n",
    "        # 将类标签和分配的边界框坐标初始化为零\n",
    "        class_labels = torch.zeros(num_anchors, dtype=torch.long,\n",
    "                                   device=device)\n",
    "        assigned_bb = torch.zeros((num_anchors, 4), dtype=torch.float32,\n",
    "                                  device=device)\n",
    "        # 使用真实边界框来标记锚框的类别。\n",
    "        # 如果一个锚框没有被分配，标记其为背景（值为零）\n",
    "        indices_true = torch.nonzero(anchors_bbox_map >= 0)\n",
    "        bb_idx = anchors_bbox_map[indices_true]\n",
    "        class_labels[indices_true] = label[bb_idx, 0].long() + 1\n",
    "        assigned_bb[indices_true] = label[bb_idx, 1:]\n",
    "        # 偏移量转换\n",
    "        offset = offset_boxes(anchors, assigned_bb) * bbox_mask\n",
    "        batch_offset.append(offset.reshape(-1))\n",
    "        batch_mask.append(bbox_mask.reshape(-1))\n",
    "        batch_class_labels.append(class_labels)\n",
    "    bbox_offset = torch.stack(batch_offset)\n",
    "    bbox_mask = torch.stack(batch_mask)\n",
    "    class_labels = torch.stack(batch_class_labels)\n",
    "    return (bbox_offset, bbox_mask, class_labels)"
   ],
   "id": "57e69b1186f23243",
   "outputs": [],
   "execution_count": 17
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:47:58.451959046Z",
     "start_time": "2026-07-27T09:47:58.310247636Z"
    }
   },
   "cell_type": "code",
   "source": [
    "ground_truth = torch.tensor([[0, 0.1, 0.08, 0.52, 0.92],\n",
    "[1, 0.55, 0.2, 0.9, 0.88]])\n",
    "anchors = torch.tensor([[0, 0.1, 0.2, 0.3], [0.15, 0.2, 0.4, 0.4],\n",
    "[0.63, 0.05, 0.88, 0.98], [0.66, 0.45, 0.8, 0.8],\n",
    "[0.57, 0.3, 0.92, 0.9]])\n",
    "fig = d2l.plt.imshow(img)\n",
    "show_bboxes(fig.axes, ground_truth[:, 1:] * bbox_scale, ['dog', 'cat'], 'k')\n",
    "show_bboxes(fig.axes, anchors * bbox_scale, ['0', '1', '2', '3', '4']);"
   ],
   "id": "260673166da2aa71",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 350x250 with 1 Axes>"
      ],
      "image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"220.346324pt\" height=\"173.353814pt\" viewBox=\"0 0 220.346324 173.353814\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n <metadata>\n  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n   <cc:Work>\n    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n    <dc:date>2026-07-27T17:47:58.388372</dc:date>\n    <dc:format>image/svg+xml</dc:format>\n    <dc:creator>\n     <cc:Agent>\n      <dc:title>Matplotlib v3.7.2, https://matplotlib.org/</dc:title>\n     </cc:Agent>\n    </dc:creator>\n   </cc:Work>\n  </rdf:RDF>\n </metadata>\n <defs>\n  <style type=\"text/css\">*{stroke-linejoin: round; stroke-linecap: butt}</style>\n </defs>\n <g id=\"figure_1\">\n  <g id=\"patch_1\">\n   <path d=\"M 0 173.353814 \nL 220.346324 173.353814 \nL 220.346324 0 \nL 0 0 \nz\n\"/>\n  </g>\n  <g id=\"axes_1\">\n   <g id=\"patch_2\">\n    <path d=\"M 33.2875 149.475689 \nL 213.146324 149.475689 \nL 213.146324 10.875689 \nL 33.2875 10.875689 \nz\n\"/>\n   </g>\n   <g clip-path=\"url(#p9228ade140)\">\n    <image xlink:href=\"data:image/png;base64,\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
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 18
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:47:58.499427639Z",
     "start_time": "2026-07-27T09:47:58.453550913Z"
    }
   },
   "cell_type": "code",
   "source": [
    "labels = multibox_target(anchors.unsqueeze(dim=0),\n",
    "            ground_truth.unsqueeze(dim=0))"
   ],
   "id": "aafe21dd7b10dde3",
   "outputs": [],
   "execution_count": 19
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:47:58.560984562Z",
     "start_time": "2026-07-27T09:47:58.500638893Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def offset_inverse(anchors, offset_preds):\n",
    "    \"\"\"根据带有预测偏移量的锚框来预测边界框\"\"\"\n",
    "    anc = d2l.box_corner_to_center(anchors)\n",
    "    pred_bbox_xy = (offset_preds[:, :2] * anc[:, 2:] / 10) + anc[:, :2]\n",
    "    pred_bbox_wh = torch.exp(offset_preds[:, 2:] / 5) * anc[:, 2:]\n",
    "    pred_bbox = torch.cat((pred_bbox_xy, pred_bbox_wh), axis=1)\n",
    "    predicted_bbox = d2l.box_center_to_corner(pred_bbox)\n",
    "    return predicted_bbox"
   ],
   "id": "f15edcb302b1f95e",
   "outputs": [],
   "execution_count": 20
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:47:58.627497913Z",
     "start_time": "2026-07-27T09:47:58.578335925Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def nms(boxes, scores, iou_threshold):\n",
    "    \"\"\"对预测边界框的置信度进行排序\"\"\"\n",
    "    B = torch.argsort(scores, dim=-1, descending=True)\n",
    "    keep = [] # 保留预测边界框的指标\n",
    "    while B.numel() > 0:\n",
    "        i = B[0]\n",
    "        keep.append(i)\n",
    "        if B.numel() == 1: break\n",
    "        iou = box_iou(boxes[i, :].reshape(-1, 4),\n",
    "                        boxes[B[1:], :].reshape(-1, 4)).reshape(-1)\n",
    "        inds = torch.nonzero(iou <= iou_threshold).reshape(-1)\n",
    "        B = B[inds + 1]\n",
    "    return torch.tensor(keep, device=boxes.device)"
   ],
   "id": "7dfcdd54114d8a06",
   "outputs": [],
   "execution_count": 21
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:47:58.687688493Z",
     "start_time": "2026-07-27T09:47:58.628509966Z"
    }
   },
   "cell_type": "code",
   "source": [
    "#@save\n",
    "def multibox_detection(cls_probs, offset_preds, anchors, nms_threshold=0.5,\n",
    "                       pos_threshold=0.009999999):\n",
    "    \"\"\"使用非极大值抑制来预测边界框\"\"\"\n",
    "    device, batch_size = cls_probs.device, cls_probs.shape[0]\n",
    "    anchors = anchors.squeeze(0)\n",
    "    num_classes, num_anchors = cls_probs.shape[1], cls_probs.shape[2]\n",
    "    out = []\n",
    "    for i in range(batch_size):\n",
    "        cls_prob, offset_pred = cls_probs[i], offset_preds[i].reshape(-1, 4)\n",
    "        conf, class_id = torch.max(cls_prob[1:], 0)\n",
    "        predicted_bb = offset_inverse(anchors, offset_pred)\n",
    "        keep = nms(predicted_bb, conf, nms_threshold)\n",
    "        # 找到所有的non_keep索引，并将类设置为背景\n",
    "        all_idx = torch.arange(num_anchors, dtype=torch.long, device=device)\n",
    "        combined = torch.cat((keep, all_idx))\n",
    "        uniques, counts = combined.unique(return_counts=True)\n",
    "        non_keep = uniques[counts == 1]\n",
    "        all_id_sorted = torch.cat((keep, non_keep))\n",
    "        class_id[non_keep] = -1\n",
    "        class_id = class_id[all_id_sorted]\n",
    "        conf, predicted_bb = conf[all_id_sorted], predicted_bb[all_id_sorted]\n",
    "        # pos_threshold是一个用于非背景预测的阈值\n",
    "        below_min_idx = (conf < pos_threshold)\n",
    "        class_id[below_min_idx] = -1\n",
    "        conf[below_min_idx] = 1 - conf[below_min_idx]\n",
    "        pred_info = torch.cat((class_id.unsqueeze(1),\n",
    "                               conf.unsqueeze(1),\n",
    "                               predicted_bb), dim=1)\n",
    "\n",
    "        out.append(pred_info)\n",
    "    return torch.stack(out)"
   ],
   "id": "8313f60149168f3d",
   "outputs": [],
   "execution_count": 22
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:47:58.737335139Z",
     "start_time": "2026-07-27T09:47:58.689268726Z"
    }
   },
   "cell_type": "code",
   "source": [
    "anchors = torch.tensor([[0.1, 0.08, 0.52, 0.92], [0.08, 0.2, 0.56, 0.95],\n",
    "[0.15, 0.3, 0.62, 0.91], [0.55, 0.2, 0.9, 0.88]])\n",
    "offset_preds = torch.tensor([0] * anchors.numel())\n",
    "cls_probs = torch.tensor([[0] * 4, # 背景的预测概率\n",
    "[0.9, 0.8, 0.7, 0.1], # 狗的预测概率\n",
    "[0.1, 0.2, 0.3, 0.9]]) # 猫的预测概率"
   ],
   "id": "46de8ece74b27875",
   "outputs": [],
   "execution_count": 23
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:47:58.871856579Z",
     "start_time": "2026-07-27T09:47:58.738750970Z"
    }
   },
   "cell_type": "code",
   "source": [
    "fig = d2l.plt.imshow(img)\n",
    "show_bboxes(fig.axes, anchors * bbox_scale,\n",
    "['dog=0.9', 'dog=0.8', 'dog=0.7', 'cat=0.9'])"
   ],
   "id": "ed43634b61e3ec27",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 350x250 with 1 Axes>"
      ],
      "image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"220.346324pt\" height=\"173.353814pt\" viewBox=\"0 0 220.346324 173.353814\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n <metadata>\n  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n   <cc:Work>\n    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n    <dc:date>2026-07-27T17:47:58.828265</dc:date>\n    <dc:format>image/svg+xml</dc:format>\n    <dc:creator>\n     <cc:Agent>\n      <dc:title>Matplotlib v3.7.2, https://matplotlib.org/</dc:title>\n     </cc:Agent>\n    </dc:creator>\n   </cc:Work>\n  </rdf:RDF>\n </metadata>\n <defs>\n  <style type=\"text/css\">*{stroke-linejoin: round; stroke-linecap: butt}</style>\n </defs>\n <g id=\"figure_1\">\n  <g id=\"patch_1\">\n   <path d=\"M 0 173.353814 \nL 220.346324 173.353814 \nL 220.346324 0 \nL 0 0 \nz\n\"/>\n  </g>\n  <g id=\"axes_1\">\n   <g id=\"patch_2\">\n    <path d=\"M 33.2875 149.475689 \nL 213.146324 149.475689 \nL 213.146324 10.875689 \nL 33.2875 10.875689 \nz\n\"/>\n   </g>\n   <g clip-path=\"url(#pf5ff0b9d7c)\">\n    <image xlink:href=\"data:image/png;base64,\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
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 24
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:47:58.961912712Z",
     "start_time": "2026-07-27T09:47:58.872770917Z"
    }
   },
   "cell_type": "code",
   "source": [
    "output = multibox_detection(cls_probs.unsqueeze(dim=0),\n",
    "offset_preds.unsqueeze(dim=0),\n",
    "anchors.unsqueeze(dim=0),\n",
    "nms_threshold=0.5)\n",
    "output"
   ],
   "id": "7eb0e18519f4b55f",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[[ 0.0000,  0.9000,  0.1000,  0.0800,  0.5200,  0.9200],\n",
       "         [ 1.0000,  0.9000,  0.5500,  0.2000,  0.9000,  0.8800],\n",
       "         [-1.0000,  0.8000,  0.0800,  0.2000,  0.5600,  0.9500],\n",
       "         [-1.0000,  0.7000,  0.1500,  0.3000,  0.6200,  0.9100]]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 25
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:47:59.200171491Z",
     "start_time": "2026-07-27T09:47:58.962631809Z"
    }
   },
   "cell_type": "code",
   "source": [
    "fig = d2l.plt.imshow(img)\n",
    "for i in output[0].detach().numpy():\n",
    "    if i[0] == -1:\n",
    "        continue\n",
    "    label = ('dog=', 'cat=')[int(i[0])] + str(i[1])\n",
    "    show_bboxes(fig.axes, [torch.tensor(i[2:]) * bbox_scale], label)"
   ],
   "id": "fec1c1f8349a44fe",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 350x250 with 1 Axes>"
      ],
      "image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"220.346324pt\" height=\"173.353814pt\" viewBox=\"0 0 220.346324 173.353814\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n <metadata>\n  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n   <cc:Work>\n    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n    <dc:date>2026-07-27T17:47:59.051198</dc:date>\n    <dc:format>image/svg+xml</dc:format>\n    <dc:creator>\n     <cc:Agent>\n      <dc:title>Matplotlib v3.7.2, https://matplotlib.org/</dc:title>\n     </cc:Agent>\n    </dc:creator>\n   </cc:Work>\n  </rdf:RDF>\n </metadata>\n <defs>\n  <style type=\"text/css\">*{stroke-linejoin: round; stroke-linecap: butt}</style>\n </defs>\n <g id=\"figure_1\">\n  <g id=\"patch_1\">\n   <path d=\"M 0 173.353814 \nL 220.346324 173.353814 \nL 220.346324 0 \nL 0 0 \nz\n\"/>\n  </g>\n  <g id=\"axes_1\">\n   <g id=\"patch_2\">\n    <path d=\"M 33.2875 149.475689 \nL 213.146324 149.475689 \nL 213.146324 10.875689 \nL 33.2875 10.875689 \nz\n\"/>\n   </g>\n   <g clip-path=\"url(#p9bf1eeea83)\">\n    <image xlink:href=\"data:image/png;base64,\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
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 26
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:47:59.227792428Z",
     "start_time": "2026-07-27T09:47:59.205845108Z"
    }
   },
   "cell_type": "code",
   "source": [
    "img = d2l.plt.imread('../Pictures/1.jpg')\n",
    "h, w = img.shape[:2]\n",
    "h, w"
   ],
   "id": "ea166e0233574bf3",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(640, 640)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 27
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:47:59.462849505Z",
     "start_time": "2026-07-27T09:47:59.228706763Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def display_anchors(fmap_w, fmap_h, s):\n",
    "    d2l.set_figsize()\n",
    "    # 前两个维度上的值不影响输出\n",
    "    fmap = torch.zeros((1, 10, fmap_h, fmap_w))\n",
    "    anchors = d2l.multibox_prior(fmap, sizes=s, ratios=[1, 2, 0.5,0.3])\n",
    "    bbox_scale = torch.tensor((w, h, w, h))\n",
    "    d2l.show_bboxes(d2l.plt.imshow(img).axes,\n",
    "        anchors[0] * bbox_scale)\n",
    "display_anchors(fmap_w=3, fmap_h=3, s=[0.15,0.2,0.3])"
   ],
   "id": "41cab7a08738ed58",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 350x250 with 1 Axes>"
      ],
      "image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"180.077031pt\" height=\"173.369063pt\" viewBox=\"0 0 180.077031 173.369063\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n <metadata>\n  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n   <cc:Work>\n    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n    <dc:date>2026-07-27T17:47:59.341993</dc:date>\n    <dc:format>image/svg+xml</dc:format>\n    <dc:creator>\n     <cc:Agent>\n      <dc:title>Matplotlib v3.7.2, https://matplotlib.org/</dc:title>\n     </cc:Agent>\n    </dc:creator>\n   </cc:Work>\n  </rdf:RDF>\n </metadata>\n <defs>\n  <style type=\"text/css\">*{stroke-linejoin: round; stroke-linecap: butt}</style>\n </defs>\n <g id=\"figure_1\">\n  <g id=\"patch_1\">\n   <path d=\"M 0 173.369063 \nL 180.077031 173.369063 \nL 180.077031 0 \nL 0 0 \nz\n\"/>\n  </g>\n  <g id=\"axes_1\">\n   <g id=\"patch_2\">\n    <path d=\"M 33.2875 149.490938 \nL 171.8875 149.490938 \nL 171.8875 10.890938 \nL 33.2875 10.890938 \nz\n\"/>\n   </g>\n   <g clip-path=\"url(#pcb3e935286)\">\n    <image xlink:href=\"data:image/png;base64,\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
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 28
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:47:59.984065826Z",
     "start_time": "2026-07-27T09:47:59.567538110Z"
    }
   },
   "cell_type": "code",
   "source": "display_anchors(fmap_w=2, fmap_h=2, s=[0.4])",
   "id": "6620db5aa275bf52",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 350x250 with 1 Axes>"
      ],
      "image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"180.077031pt\" height=\"173.369063pt\" viewBox=\"0 0 180.077031 173.369063\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n <metadata>\n  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n   <cc:Work>\n    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n    <dc:date>2026-07-27T17:47:59.675822</dc:date>\n    <dc:format>image/svg+xml</dc:format>\n    <dc:creator>\n     <cc:Agent>\n      <dc:title>Matplotlib v3.7.2, https://matplotlib.org/</dc:title>\n     </cc:Agent>\n    </dc:creator>\n   </cc:Work>\n  </rdf:RDF>\n </metadata>\n <defs>\n  <style type=\"text/css\">*{stroke-linejoin: round; stroke-linecap: butt}</style>\n </defs>\n <g id=\"figure_1\">\n  <g id=\"patch_1\">\n   <path d=\"M 0 173.369063 \nL 180.077031 173.369063 \nL 180.077031 0 \nL 0 0 \nz\n\"/>\n  </g>\n  <g id=\"axes_1\">\n   <g id=\"patch_2\">\n    <path d=\"M 33.2875 149.490938 \nL 171.8875 149.490938 \nL 171.8875 10.890938 \nL 33.2875 10.890938 \nz\n\"/>\n   </g>\n   <g clip-path=\"url(#p15c37a89fa)\">\n    <image xlink:href=\"data:image/png;base64,\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
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 29
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:48:00.334968551Z",
     "start_time": "2026-07-27T09:48:00.005932344Z"
    }
   },
   "cell_type": "code",
   "source": "display_anchors(fmap_w=1, fmap_h=1, s=[0.8])",
   "id": "8a0c4555b2752c99",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 350x250 with 1 Axes>"
      ],
      "image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"180.077031pt\" height=\"173.369063pt\" viewBox=\"0 0 180.077031 173.369063\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n <metadata>\n  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n   <cc:Work>\n    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n    <dc:date>2026-07-27T17:48:00.079197</dc:date>\n    <dc:format>image/svg+xml</dc:format>\n    <dc:creator>\n     <cc:Agent>\n      <dc:title>Matplotlib v3.7.2, https://matplotlib.org/</dc:title>\n     </cc:Agent>\n    </dc:creator>\n   </cc:Work>\n  </rdf:RDF>\n </metadata>\n <defs>\n  <style type=\"text/css\">*{stroke-linejoin: round; stroke-linecap: butt}</style>\n </defs>\n <g id=\"figure_1\">\n  <g id=\"patch_1\">\n   <path d=\"M 0 173.369063 \nL 180.077031 173.369063 \nL 180.077031 0 \nL 0 0 \nz\n\"/>\n  </g>\n  <g id=\"axes_1\">\n   <g id=\"patch_2\">\n    <path d=\"M 33.2875 149.490938 \nL 171.8875 149.490938 \nL 171.8875 10.890938 \nL 33.2875 10.890938 \nz\n\"/>\n   </g>\n   <g clip-path=\"url(#pb525e67899)\">\n    <image xlink:href=\"data:image/png;base64,\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
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 30
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:48:00.402774849Z",
     "start_time": "2026-07-27T09:48:00.390428177Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import torchvision,os\n",
    "import pandas as pd\n",
    "def read_data_bananas(is_train=True):\n",
    "    \"\"\"读取香蕉检测数据集中的图像和标签\"\"\"\n",
    "    data_dir = d2l.download_extract('banana-detection')\n",
    "    csv_fname = os.path.join(data_dir, 'bananas_train' if is_train\n",
    "    else 'bananas_val', 'label.csv')\n",
    "    csv_data = pd.read_csv(csv_fname)\n",
    "    csv_data = csv_data.set_index('img_name')\n",
    "    images, targets = [], []\n",
    "    for img_name, target in csv_data.iterrows():\n",
    "        images.append(torchvision.io.read_image(\n",
    "            os.path.join(data_dir, 'bananas_train' if is_train else\n",
    "                    'bananas_val', 'images', f'{img_name}')))\n",
    "        # 这里的target包含（类别，左上角x，左上角y，右下角x，右下角y），\n",
    "        # 其中所有图像都具有相同的香蕉类（索引为0）\n",
    "        targets.append(list(target))\n",
    "    return images, torch.tensor(targets).unsqueeze(1) / 256"
   ],
   "id": "70e7bc1342f90cea",
   "outputs": [],
   "execution_count": 31
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:48:00.463250908Z",
     "start_time": "2026-07-27T09:48:00.403783355Z"
    }
   },
   "cell_type": "code",
   "source": [
    "class BananasDataset(torch.utils.data.Dataset):\n",
    "    \"\"\"一个用于加载香蕉检测数据集的自定义数据集\"\"\"\n",
    "    def __init__(self, is_train):\n",
    "        self.features, self.labels = read_data_bananas(is_train)\n",
    "        print('read ' + str(len(self.features)) + (f' training examples' if\n",
    "                    is_train else f' validation examples'))\n",
    "    def __getitem__(self, idx):\n",
    "        return (self.features[idx].float(), self.labels[idx])\n",
    "    def __len__(self):\n",
    "        return len(self.features)\n",
    "def load_data_bananas(batch_size):\n",
    "    \"\"\"加载香蕉检测数据集\"\"\"\n",
    "    train_iter = torch.utils.data.DataLoader(BananasDataset(is_train=True),\n",
    "        batch_size, shuffle=True)\n",
    "    val_iter = torch.utils.data.DataLoader(BananasDataset(is_train=False),\n",
    "        batch_size)\n",
    "    return train_iter, val_iter"
   ],
   "id": "1c80340fca8af59a",
   "outputs": [],
   "execution_count": 32
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:48:03.208374192Z",
     "start_time": "2026-07-27T09:48:00.491960801Z"
    }
   },
   "cell_type": "code",
   "source": [
    "batch_size, edge_size = 32, 256\n",
    "train_iter, _ = load_data_bananas(batch_size)\n",
    "batch = next(iter(train_iter))\n",
    "batch[0].shape, batch[1].shape"
   ],
   "id": "e6aacbbedaa732f6",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "read 1000 training examples\n",
      "read 100 validation examples\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(torch.Size([32, 3, 256, 256]), torch.Size([32, 1, 5]))"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 33
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:48:03.533990096Z",
     "start_time": "2026-07-27T09:48:03.269951948Z"
    }
   },
   "cell_type": "code",
   "source": [
    "imgs = (batch[0][0:10].permute(0, 2, 3, 1)) / 255\n",
    "axes = d2l.show_images(imgs, 2, 5, scale=2)\n",
    "for ax, label in zip(axes, batch[1][0:10]):\n",
    "    d2l.show_bboxes(ax, [label[0][1:5] * edge_size], colors=['b'])"
   ],
   "id": "528cb4f32e152b5",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x400 with 10 Axes>"
      ],
      "image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"572.4pt\" height=\"231.566897pt\" viewBox=\"0 0 572.4 231.566897\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n <metadata>\n  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n   <cc:Work>\n    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n    <dc:date>2026-07-27T17:48:03.414413</dc:date>\n    <dc:format>image/svg+xml</dc:format>\n    <dc:creator>\n     <cc:Agent>\n      <dc:title>Matplotlib v3.7.2, https://matplotlib.org/</dc:title>\n     </cc:Agent>\n    </dc:creator>\n   </cc:Work>\n  </rdf:RDF>\n </metadata>\n <defs>\n  <style type=\"text/css\">*{stroke-linejoin: round; stroke-linecap: butt}</style>\n </defs>\n <g id=\"figure_1\">\n  <g id=\"patch_1\">\n   <path d=\"M 0 231.566897 \nL 572.4 231.566897 \nL 572.4 0 \nL 0 0 \nz\n\"/>\n  </g>\n  <g id=\"axes_1\">\n   <g id=\"patch_2\">\n    <path d=\"M 7.2 103.406897 \nL 103.406897 103.406897 \nL 103.406897 7.2 \nL 7.2 7.2 \nz\n\"/>\n   </g>\n   <g clip-path=\"url(#pfeae1e10d8)\">\n    <image xlink:href=\"data:image/png;base64,\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
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 34
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:48:03.590014764Z",
     "start_time": "2026-07-27T09:48:03.541625963Z"
    }
   },
   "cell_type": "code",
   "source": [
    "from torch import nn\n",
    "from torch.nn import functional as F\n",
    "def cls_predictor(num_inputs,num_anchors,num_classes):\n",
    "    return nn.Conv2d(num_inputs,num_anchors*(num_classes+1), kernel_size=3,padding=1)\n",
    "# 不改变原来图像的面积，提升通道数，每一个通道对应的是每一种锚框的一种类别的可能性\n",
    "def bbox_predictor(num_inputs, num_anchors):\n",
    "    return nn.Conv2d(num_inputs, num_anchors * 4, kernel_size=3, padding=1)\n",
    "# 不改变原来图像的面积，提升通道数，每一个通道对应的是每一种锚框距离正确标记框的偏移量\n"
   ],
   "id": "eb1131ed49817939",
   "outputs": [],
   "execution_count": 35
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:48:03.659914611Z",
     "start_time": "2026-07-27T09:48:03.591656234Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def forward(x, block):\n",
    "    return block(x)\n",
    "Y1 = forward(torch.zeros((2, 8, 20, 20)), cls_predictor(8, 5, 10))\n",
    "Y2 = forward(torch.zeros((2, 16, 10, 10)), cls_predictor(16, 3, 10))\n",
    "Y1.shape, Y2.shape\n",
    "#类别预测输出中的通道数分别为5 × (10 + 1) = 55和3 × (10 + 1) = 33，其中任一输出的形\n",
    "#状是（批量大小，通道数，高度，宽度）"
   ],
   "id": "f2a7c69cdd4aafa6",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([2, 55, 20, 20]), torch.Size([2, 33, 10, 10]))"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 36
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "为了方便不同类别的图像进行训练，我们要把张量拍平再cat",
   "id": "47e46c98c2e7d5e2"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:48:03.761906859Z",
     "start_time": "2026-07-27T09:48:03.661658265Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def flatten_pred(pred):\n",
    "    #要先调换维数才能拍平 0 2 3 1 (batch w h channel)\n",
    "    return torch.flatten(pred.permute(0,2,3,1), start_dim=1)\n",
    "def concat_preds(preds):\n",
    "    return torch.cat([flatten_pred(p) for p in preds], dim=1)\n",
    "concat_preds([Y1, Y2]).shape\n"
   ],
   "id": "60a8cd1d9e8c1ad5",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([2, 25300])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 37
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "下采样 提高感受野提高大物品的识别能力",
   "id": "cb572fcd8e8d90a7"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:48:03.827127144Z",
     "start_time": "2026-07-27T09:48:03.784059223Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def down_sample_blk(in_channels,out_channels):\n",
    "    blk = []\n",
    "    for _ in range(2):\n",
    "        blk.append(nn.Conv2d(in_channels, out_channels, kernel_size=3, padding=1)) #不改变大小 提升通道数哈 传统VGG做法\n",
    "        blk.append(nn.BatchNorm2d(out_channels))\n",
    "        blk.append(nn.ReLU())\n",
    "        in_channels = out_channels\n",
    "    blk.append(nn.MaxPool2d(2)) #降维\n",
    "    return nn.Sequential(*blk)"
   ],
   "id": "a591f38441189d0c",
   "outputs": [],
   "execution_count": 38
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:48:03.921203148Z",
     "start_time": "2026-07-27T09:48:03.827866637Z"
    }
   },
   "cell_type": "code",
   "source": [
    "forward(torch.zeros((2, 3, 20, 20)), down_sample_blk(3, 10)).shape\n",
    "#降维升channel"
   ],
   "id": "8a771cd261a46563",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([2, 10, 10, 10])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 39
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:48:04.128732201Z",
     "start_time": "2026-07-27T09:48:03.922820914Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def base_net():\n",
    "    blk = []\n",
    "    num_filters = [3,16,32,64]\n",
    "    for i in range(len(num_filters)-1):\n",
    "        blk.append(down_sample_blk(num_filters[i], num_filters[i+1]))\n",
    "    return nn.Sequential(*blk)\n",
    "\n",
    "forward(torch.zeros((2, 3, 256, 256)), base_net()).shape"
   ],
   "id": "d10ba91021ef0d0c",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([2, 64, 32, 32])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 40
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:48:04.177851376Z",
     "start_time": "2026-07-27T09:48:04.129824175Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def get_blk(i):\n",
    "    if i == 0:\n",
    "        blk = base_net()\n",
    "    elif i == 1:\n",
    "        blk = down_sample_blk(64, 128)\n",
    "    elif i == 4:\n",
    "        blk = nn.AdaptiveMaxPool2d((1,1))\n",
    "    else:\n",
    "        blk = down_sample_blk(128, 128)\n",
    "    return blk"
   ],
   "id": "c17a584cd71a450a",
   "outputs": [],
   "execution_count": 41
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:48:04.244078688Z",
     "start_time": "2026-07-27T09:48:04.179531133Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def blk_forward(X,blk,size,ratio,cls_predictor,bbox_predictor):\n",
    "    Y =blk(X)\n",
    "    anchors = d2l.multibox_prior(Y,sizes=size,ratios=ratio)\n",
    "    cls_preds = cls_predictor(Y)\n",
    "    bbox_preds = bbox_predictor(Y)\n",
    "    return (Y,anchors,cls_preds,bbox_preds)\n",
    "\"\"\"\n",
    "Y : CNN特征图\n",
    "anchors : 在当前尺度下生成的锚框\n",
    "cls_preds :每个锚框的类别\n",
    "bbox_preds :每个锚框的偏移量\n",
    "\"\"\""
   ],
   "id": "d686dd6c196b17a1",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\nY : CNN特征图\\nanchors : 在当前尺度下生成的锚框\\ncls_preds :每个锚框的类别\\nbbox_preds :每个锚框的偏移量\\n'"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 42
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:48:04.311459490Z",
     "start_time": "2026-07-27T09:48:04.245645919Z"
    }
   },
   "cell_type": "code",
   "source": [
    "sizes = [[0.2, 0.272], [0.37, 0.447], [0.54, 0.619], [0.71, 0.79],\n",
    "        [0.88, 0.961]]\n",
    "ratios = [[1, 2, 0.5]] * 5\n",
    "num_anchors = len(sizes[0]) + len(ratios[0]) - 1"
   ],
   "id": "24fbc8fb3e72cbaf",
   "outputs": [],
   "execution_count": 43
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:48:04.357710443Z",
     "start_time": "2026-07-27T09:48:04.348460151Z"
    }
   },
   "cell_type": "code",
   "source": [
    "class TinySSD(nn.Module):\n",
    "    def __init__(self,num_classes,**kwargs):\n",
    "        super(TinySSD,self).__init__(**kwargs)\n",
    "        self.num_classes = num_classes\n",
    "        idx_to_in_channels = [64,128,128,128,128]\n",
    "        for i in range(5):\n",
    "            setattr(self,f\"blk_{i}\",get_blk(i))\n",
    "            setattr(self,f\"cls_{i}\",cls_predictor(idx_to_in_channels[i],num_anchors,num_classes))\n",
    "            setattr(self, f'bbox_{i}', bbox_predictor(idx_to_in_channels[i],num_anchors))\n",
    "    def forward(self,X):\n",
    "        anchors,cls_preds,bbox_preds=[None]*5,[None]*5,[None]*5\n",
    "        for i in range(5):\n",
    "            X,anchors[i],cls_preds[i],bbox_preds[i]=blk_forward(X,getattr(self,f'blk_{i}'),sizes[i],ratios[i],getattr(self, f'cls_{i}'), getattr(self, f'bbox_{i}'))\n",
    "        anchors = torch.cat(anchors,dim=1)\n",
    "        cls_preds = concat_preds(cls_preds)\n",
    "        cls_preds = cls_preds.reshape(cls_preds.shape[0],-1,self.num_classes+1)\n",
    "        bbox_preds = concat_preds(bbox_preds)\n",
    "        return anchors,cls_preds,bbox_preds"
   ],
   "id": "642c9acb03ef05af",
   "outputs": [],
   "execution_count": 44
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "应该是生成(32^2 + 16^2 + 8^2 + 4^2 + 1) × 4 = 5444个锚框\n",
   "id": "bb9119aecefba2b9"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:48:05.245395003Z",
     "start_time": "2026-07-27T09:48:04.358575367Z"
    }
   },
   "cell_type": "code",
   "source": [
    "net = TinySSD(num_classes=1)\n",
    "X = torch.zeros((32, 3, 256, 256))\n",
    "anchors, cls_preds, bbox_preds = net(X)\n",
    "print('output anchors:', anchors.shape)\n",
    "print('output class preds:', cls_preds.shape)\n",
    "print('output bbox preds:', bbox_preds.shape)"
   ],
   "id": "c0f4abb77f5df63f",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "output anchors: torch.Size([1, 5444, 4])\n",
      "output class preds: torch.Size([32, 5444, 2])\n",
      "output bbox preds: torch.Size([32, 21776])\n"
     ]
    }
   ],
   "execution_count": 45
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:48:08.014082271Z",
     "start_time": "2026-07-27T09:48:05.279839380Z"
    }
   },
   "cell_type": "code",
   "source": [
    "batch_size = 32\n",
    "train_iter, _ = d2l.load_data_bananas(batch_size)"
   ],
   "id": "8cdaf93f4dce3208",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "read 1000 training examples\n",
      "read 100 validation examples\n"
     ]
    }
   ],
   "execution_count": 46
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:48:08.178564673Z",
     "start_time": "2026-07-27T09:48:08.120907893Z"
    }
   },
   "cell_type": "code",
   "source": [
    "device, net = d2l.try_gpu(), TinySSD(num_classes=1)\n",
    "trainer = torch.optim.SGD(net.parameters(), lr=0.2, weight_decay=5e-4)"
   ],
   "id": "4d40936938c9b028",
   "outputs": [],
   "execution_count": 47
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:48:08.336189213Z",
     "start_time": "2026-07-27T09:48:08.180393347Z"
    }
   },
   "cell_type": "code",
   "source": [
    "\n",
    "cls_loss = nn.CrossEntropyLoss(reduction='none')\n",
    "bbox_loss = nn.L1Loss(reduction='none')\n",
    "def calc_loss(cls_preds,cls_labels,bbox_preds,bbox_labels,bbox_masks):\n",
    "    batch_size,num_classes = cls_preds.shape[0] , cls_preds.shape[2]\n",
    "    cls = cls_loss(cls_preds.reshape(-1,num_classes),cls_labels.reshape(-1)).reshape(batch_size,-1).mean(dim=1)\n",
    "    bbox = bbox_loss(bbox_preds*bbox_masks,bbox_labels*bbox_masks).mean(dim=1)\n",
    "    return cls + bbox"
   ],
   "id": "8e07cd2f6db67147",
   "outputs": [],
   "execution_count": 48
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:48:08.399558542Z",
     "start_time": "2026-07-27T09:48:08.343338340Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 验证 类别预测用acc 锚框偏移量预测用L1范数\n",
    "def cls_eval(cls_preds,cls_labels)->float:\n",
    "    return float((cls_preds.argmax(dim=-1).type(cls_labels.dtype)==cls_labels).sum())\n",
    "def bbox_eval(bbox_preds, bbox_labels, bbox_masks):\n",
    "    return float((torch.abs((bbox_labels - bbox_preds) * bbox_masks)).sum())"
   ],
   "id": "e2dd1576866afef9",
   "outputs": [],
   "execution_count": 49
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:50:07.366475114Z",
     "start_time": "2026-07-27T09:48:08.401037720Z"
    }
   },
   "cell_type": "code",
   "source": [
    "num_epochs, timer = 20, d2l.Timer()\n",
    "animator = d2l.Animator(xlabel='epoch', xlim=[1, num_epochs],\n",
    "legend=['class error', 'bbox mae'])\n",
    "net = net.to(device)\n",
    "for epoch in range(num_epochs):\n",
    "    metric = d2l.Accumulator(4)\n",
    "    net.train()\n",
    "    for feature , target in train_iter:\n",
    "    # feature -> (batch,3,h,w) target (batch,num,5) 其中5维数据分别为 label h1 w1 h2 w2\n",
    "        timer.start()\n",
    "        trainer.zero_grad()\n",
    "        X,Y=feature.to(device),target.to(device)\n",
    "        anchors,cls_preds,bbox_preds = net(X)\n",
    "        bbox_labels, bbox_masks, cls_labels = d2l.multibox_target(anchors, Y)\n",
    "        l = calc_loss(cls_preds, cls_labels, bbox_preds, bbox_labels,\n",
    "            bbox_masks)\n",
    "        l.mean().backward()\n",
    "        trainer.step()\n",
    "        metric.add(cls_eval(cls_preds, cls_labels), cls_labels.numel(),\n",
    "                    bbox_eval(bbox_preds, bbox_labels, bbox_masks),\n",
    "                        bbox_labels.numel())\n",
    "        #计数器依次是 cls正确率 分类任务总个数 box偏移量l1范数 框选任务总个数\n",
    "    cls_err, bbox_mae = 1 - metric[0] / metric[1], metric[2] / metric[3]\n",
    "    animator.add(epoch + 1, (cls_err, bbox_mae))\n",
    "print(f'class err {cls_err:.2e}, bbox mae {bbox_mae:.2e}')"
   ],
   "id": "720fb1fc6b3bfaed",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "class err 3.31e-03, bbox mae 3.15e-03\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 350x250 with 1 Axes>"
      ],
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     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 50
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:50:07.767970800Z",
     "start_time": "2026-07-27T09:50:07.458706602Z"
    }
   },
   "cell_type": "code",
   "source": [
    "X = torchvision.io.read_image('../data/banana.jpg').unsqueeze(0).float()\n",
    "img = X.squeeze(0).permute(1,2,0).long()\n"
   ],
   "id": "b6a5ae7b16b60e50",
   "outputs": [],
   "execution_count": 51
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:50:08.153935112Z",
     "start_time": "2026-07-27T09:50:07.880617944Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def predict(X):\n",
    "    net.eval()\n",
    "    anchors, cls_preds, bbox_preds = net(X.to(device))\n",
    "    cls_probs = F.softmax(cls_preds, dim=2).permute(0, 2, 1)\n",
    "    output = d2l.multibox_detection(cls_probs, bbox_preds, anchors)\n",
    "    idx = [i for i, row in enumerate(output[0]) if row[0] != -1]\n",
    "    return output[0, idx]\n",
    "output = predict(X)"
   ],
   "id": "64a9460651b1b585",
   "outputs": [],
   "execution_count": 52
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:50:08.240708202Z",
     "start_time": "2026-07-27T09:50:08.155681155Z"
    }
   },
   "cell_type": "code",
   "source": "output",
   "id": "e8dc16888118c7bc",
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "        [ 0.0000,  0.0131, -0.1225, -0.3201,  0.2735,  0.4565],\n",
       "        [ 0.0000,  0.0130,  0.4430,  0.5082,  1.2768,  1.2750],\n",
       "        [ 0.0000,  0.0125,  0.1837,  0.7573,  0.3872,  0.9679],\n",
       "        [ 0.0000,  0.0123,  0.4169,  0.4787,  0.5627,  0.7412],\n",
       "        [ 0.0000,  0.0122,  0.7223,  0.2193,  0.9493,  0.4536],\n",
       "        [ 0.0000,  0.0121,  0.4850,  0.4219,  0.7411,  0.6612],\n",
       "        [ 0.0000,  0.0112,  0.6911,  0.4813,  0.9275,  0.7128],\n",
       "        [ 0.0000,  0.0105,  0.5652,  0.7101,  0.7331,  0.9001],\n",
       "        [ 0.0000,  0.0102,  0.0054,  0.8066,  0.2270,  0.9863],\n",
       "        [ 0.0000,  0.0101,  0.6626,  0.0780,  0.8909,  0.3222]],\n",
       "       device='cuda:0', grad_fn=<IndexBackward0>)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 53
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-27T09:50:08.489689738Z",
     "start_time": "2026-07-27T09:50:08.274956342Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def display(img, output, threshold):\n",
    "    d2l.set_figsize((5, 5))\n",
    "    fig = d2l.plt.imshow(img)\n",
    "    for row in output:\n",
    "        score = float(row[1])\n",
    "        if score < threshold:\n",
    "            continue\n",
    "        h, w = img.shape[0:2]\n",
    "        bbox = [row[2:6] * torch.tensor((w, h, w, h), device=row.device)]\n",
    "        d2l.show_bboxes(fig.axes, bbox, '%.2f' % score, 'w')\n",
    "display(img, output.cpu(), threshold=0.9)"
   ],
   "id": "add91b659a0efa1c",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([0.0000, 0.9985, 0.0642, 0.7531, 0.2869, 0.9532],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([0.0000, 0.9973, 0.4608, 0.5666, 0.6662, 0.7837],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([0.0000, 0.9970, 0.5375, 0.0591, 0.7508, 0.2796],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([0.0000, 0.9902, 0.7037, 0.3652, 0.9121, 0.5747],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([0.0000, 0.4860, 0.5226, 0.0069, 0.7186, 0.2129],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([0.0000, 0.4443, 0.4504, 0.6233, 0.6205, 0.8134],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([0.0000, 0.2552, 0.5831, 0.0923, 0.8302, 0.3042],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([ 0.0000,  0.2356,  0.5915, -0.0019,  0.7679,  0.2016],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([0.0000, 0.2331, 0.4954, 0.6350, 0.7170, 0.8248],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([0.0000, 0.1502, 0.7096, 0.2895, 0.8824, 0.5102],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([0.0000, 0.1475, 0.1230, 0.7664, 0.3295, 0.9989],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([ 0.0000,  0.1150,  0.5567, -0.0957,  0.7636,  0.1090],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([0.0000, 0.1137, 0.1259, 0.6939, 0.3409, 0.9125],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([0.0000, 0.1115, 0.4028, 0.6006, 0.5825, 0.7848],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([0.0000, 0.1093, 0.4543, 0.5068, 0.7193, 0.7340],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([0.0000, 0.1016, 0.5291, 0.1110, 0.7004, 0.3227],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([0.0000, 0.0900, 0.4455, 0.4652, 0.6391, 0.6875],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([0.0000, 0.0780, 0.4589, 0.6589, 0.6681, 0.8913],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([0.0000, 0.0652, 0.5598, 0.1803, 0.7430, 0.3703],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([0.0000, 0.0605, 0.6292, 0.3817, 0.8251, 0.5817],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([0.0000, 0.0514, 0.4952, 0.7167, 0.6964, 0.9586],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([0.0000, 0.0469, 0.6734, 0.4222, 0.8798, 0.6158],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([0.0000, 0.0416, 0.4532, 0.0716, 0.6357, 0.2691],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([ 0.0000,  0.0391,  0.4798, -0.0191,  0.6770,  0.1747],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([0.0000, 0.0389, 0.0044, 0.7313, 0.1998, 0.9244],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([0.0000, 0.0389, 0.5262, 0.4644, 0.6896, 0.6895],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([0.0000, 0.0374, 0.6148, 0.1649, 0.7902, 0.3841],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([0.0000, 0.0359, 0.0650, 0.8109, 0.2880, 1.0482],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([0.0000, 0.0359, 0.0698, 0.6747, 0.2262, 0.9140],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([ 0.0000,  0.0319,  0.6276, -0.1184,  0.7822,  0.1588],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([ 0.0000,  0.0319, -0.1519,  0.2342,  1.2012,  0.8651],\n",
      "       grad_fn=<UnbindBackward0>)\n",
      "tensor([0.0000, 0.0285, 0.1491, 0.6391, 0.3408, 0.8407],\n",
      "       grad_fn=<UnbindBackward0>)\n",
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      "       grad_fn=<UnbindBackward0>)\n",
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   "execution_count": 54
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   },
   "cell_type": "code",
   "source": "",
   "id": "4ec2f61624100d07",
   "outputs": [],
   "execution_count": 54
  }
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