你真的理解Faster RCNN吗？捋一捋Pytorch官方Faster RCNN代码

目前 pytorch 已经在 torchvision 模块集成了 FasterRCNN 和 MaskRCNN 代码。考虑到帮助各位小伙伴理解模型细节问题，本文分析一下 FasterRCNN 代码，帮助新手理解 Two-Stage 检测中的主要问题。

这篇文章默认读者已经对 FasterRCNN 原理有一定了解。否则请先点击阅读上一篇文章：

白裳： 一文读懂Faster RCNN

torchvision 中 FasterRCNN 代码文档如下：

https://pytorch.org/docs/stable/torchvision/models.html#faster-r-cnnpytorch.org

在 python 中装好 torchvision 后，输入以下命令即可查看版本和代码位置：

import torchvision

print(torchvision.__version__)
# '0.6.0'
print(torchvision.__path__) 
# ['/usr/local/lib/python3.7/site-packages/torchvision']

代码结构

图1

作为 torchvision 中目标检测基类，GeneralizedRCNN 继承了 torch.nn.Module，后续 FasterRCNN 、MaskRCNN 都继承 GeneralizedRCNN。

GeneralizedRCNN

GeneralizedRCNN 继承基类 nn.Module 。首先来看看基类 GeneralizedRCNN 的代码：

class GeneralizedRCNN(nn.Module):
    def __init__(self, backbone, rpn, roi_heads, transform):
        super(GeneralizedRCNN, self).__init__()
        self.transform = transform
        self.backbone = backbone
        self.rpn = rpn
        self.roi_heads = roi_heads
        # used only on torchscript mode
        self._has_warned = False

    @torch.jit.unused
    def eager_outputs(self, losses, detections):
        # type: (Dict[str, Tensor], List[Dict[str, Tensor]]) -> Tuple[Dict[str, Tensor], List[Dict[str, Tensor]]]
        if self.training:
            return losses

        return detections

    def forward(self, images, targets=None):
        if self.training and targets is None:
            raise ValueError("In training mode, targets should be passed")
        original_image_sizes = torch.jit.annotate(List[Tuple[int, int]], [])
        for img in images:
            val = img.shape[-2:]
            assert len(val) == 2
            original_image_sizes.append((val[0], val[1]))

        images, targets = self.transform(images, targets)
        features = self.backbone(images.tensors)
        if isinstance(features, torch.Tensor):
            features = OrderedDict([('0', features)])
        proposals, proposal_losses = self.rpn(images, features, targets)
        detections, detector_losses = self.roi_heads(features, proposals, images.image_sizes, targets)
        detections = self.transform.postprocess(detections, images.image_sizes, original_image_sizes)

        losses = {}
        losses.update(detector_losses)
        losses.update(proposal_losses)

        if torch.jit.is_scripting():
            if not self._has_warned:
                warnings.warn("RCNN always returns a (Losses, Detections) tuple in scripting")
                self._has_warned = True
            return (losses, detections)
        else:
            return self.eager_outputs(losses, detections)

对于 GeneralizedRCNN 类，其中有4个重要的接口：

1. transform

2. backbone

3. rpn

4. roi_heads

transform

# GeneralizedRCNN.forward(...)
for img in images:
    val = img.shape[-2:]
    assert len(val) == 2
    original_image_sizes.append((val[0], val[1]))

images, targets = self.transform(images, targets)

图2 transform接口

transform主要做2件事：

1. 将输入进行标准化（如FasterRCNN是对输入减 image_mean 再除 image_std）

2. 将图像缩放到固定大小（同时也要对应缩放 targets 中标记框 ）

需要说明，由于把缩放后的图像输入网络，那么网络输出的检测框也是在缩放后的图像上的。但是实际中我们需要的是在原始图像的检测框，为了对应起来，所以需要记录变换前original_images_sizes 。

图3

这里解释一下为何要缩放图像。对于 FasterRCNN，从纯理论上来说确实可以支持任意大小的图片。但是实际中，如果输入图像太大（如6000x4000）会直接撑爆内存。考虑到工程问题，缩放是一个比较稳妥的折衷选择。

backbone + rpn + roi_heads

图4

完成图像缩放之后其实才算是正式进入网络流程。接下来有4个步骤：

• 将 transform 后的图像输入到 backbone 模块提取特征图

# GeneralizedRCNN.forward(...)
features = self.backbone(images.tensors)

backbone 一般为 VGG、ResNet、MobileNet 等网络。

• 然后经过 rpn 模块生成 proposals 和 proposal_losses

# GeneralizedRCNN.forward(...)
features = self.backbone(images.tensors)

• 接着进入 roi_heads 模块（即 roi_pooling + 分类）

# GeneralizedRCNN.forward(...)
detections, detector_losses = 
        self.roi_heads(features, proposals, images.image_sizes, targets

• 最后经 postprocess 模块（进行 NMS，同时将 box 通过 original_images_size映射回原图）

# GeneralizedRCNN.forward(...)
detections = self.transform.postprocess(detections, images.image_sizes, original_image_sizes)

FasterRCNN

FasterRCNN 继承基类 GeneralizedRCNN。

class FasterRCNN(GeneralizedRCNN):

    def __init__(self, backbone, num_classes=None,
                 # transform parameters
                 min_size=800, max_size=1333,
                 image_mean=None, image_std=None,
                 # RPN parameters
                 rpn_anchor_generator=None, rpn_head=None,
                 rpn_pre_nms_top_n_train=2000, rpn_pre_nms_top_n_test=1000,
                 rpn_post_nms_top_n_train=2000, rpn_post_nms_top_n_test=1000,
                 rpn_nms_thresh=0.7,
                 rpn_fg_iou_thresh=0.7, rpn_bg_iou_thresh=0.3,
                 rpn_batch_size_per_image=256, rpn_positive_fraction=0.5,
                 # Box parameters
                 box_roi_pool=None, box_head=None, box_predictor=None,
                 box_score_thresh=0.05, box_nms_thresh=0.5, box_detections_per_img=100,
                 box_fg_iou_thresh=0.5, box_bg_iou_thresh=0.5,
                 box_batch_size_per_image=512, box_positive_fraction=0.25,
                 bbox_reg_weights=None):

        out_channels = backbone.out_channels

        if rpn_anchor_generator is None:
            anchor_sizes = ((32,), (64,), (128,), (256,), (512,))
            aspect_ratios = ((0.5, 1.0, 2.0),) * len(anchor_sizes)
            rpn_anchor_generator = AnchorGenerator(
                anchor_sizes, aspect_ratios
            )
        if rpn_head is None:
            rpn_head = RPNHead(
                out_channels, rpn_anchor_generator.num_anchors_per_location()[0]
            )

        rpn_pre_nms_top_n = dict(training=rpn_pre_nms_top_n_train, testing=rpn_pre_nms_top_n_test)
        rpn_post_nms_top_n = dict(training=rpn_post_nms_top_n_train, testing=rpn_post_nms_top_n_test)

        rpn = RegionProposalNetwork(
            rpn_anchor_generator, rpn_head,
            rpn_fg_iou_thresh, rpn_bg_iou_thresh,
            rpn_batch_size_per_image, rpn_positive_fraction,
            rpn_pre_nms_top_n, rpn_post_nms_top_n, rpn_nms_thresh)

        if box_roi_pool is None:
            box_roi_pool = MultiScaleRoIAlign(
                featmap_names=['0', '1', '2', '3'],
                output_size=7,
                sampling_ratio=2)

        if box_head is None:
            resolution = box_roi_pool.output_size[0]
            representation_size = 1024
            box_head = TwoMLPHead(
                out_channels * resolution ** 2,
                representation_size)

        if box_predictor is None:
            representation_size = 1024
            box_predictor = FastRCNNPredictor(
                representation_size,
                num_classes)

        roi_heads = RoIHeads(
            # Box
            box_roi_pool, box_head, box_predictor,
            box_fg_iou_thresh, box_bg_iou_thresh,
            box_batch_size_per_image, box_positive_fraction,
            bbox_reg_weights,
            box_score_thresh, box_nms_thresh, box_detections_per_img)

        if image_mean is None:
            image_mean = [0.485, 0.456, 0.406]
        if image_std is None:
            image_std = [0.229, 0.224, 0.225]
        transform = GeneralizedRCNNTransform(min_size, max_size, image_mean, image_std)

        super(FasterRCNN, self).__init__(backbone, rpn, roi_heads, transform)

FasterRCNN 实现了 GeneralizedRCNN 中的 transform、backbone、rpn、roi_heads 接口：

# FasterRCNN.__init__(...)
super(FasterRCNN, self).__init__(backbone, rpn, roi_heads, transform)

对于 transform 接口，使用 GeneralizedRCNNTransform 实现。从代码变量名可以明显看到包含：

• 与缩放相关参数：min_size + max_size

• 与归一化相关参数：image_mean + image_std（对输入[0, 1]减去image_mean再除以image_std）

# FasterRCNN.__init__(...)
if image_mean is None:
    image_mean = [0.485, 0.456, 0.406]
if image_std is None:
    image_std = [0.229, 0.224, 0.225]
transform = GeneralizedRCNNTransform(min_size, max_size, image_mean, image_std)

对于 backbone 使用 ResNet50 + FPN 结构：

def fasterrcnn_resnet50_fpn(pretrained=False, progress=True, num_classes=91, pretrained_backbone=True, **kwargs):
    if pretrained:
        # no need to download the backbone if pretrained is set
        pretrained_backbone = False
    backbone = resnet_fpn_backbone('resnet50', pretrained_backbone)
    model = FasterRCNN(backbone, num_classes, **kwargs)
    if pretrained:
        state_dict = load_state_dict_from_url(model_urls['fasterrcnn_resnet50_fpn_coco'], progress=progress)
        model.load_state_dict(state_dict)
    return model

ResNet: Deep Residual Learning for Image Recognition

FPN: Feature Pyramid Networks for Object Detection

图5 FPN

接下来重点介绍 rpn 接口的实现。首先是 rpn_anchor_generator :

# FasterRCNN.__init__(...)
if rpn_anchor_generator is None:
    anchor_sizes = ((32,), (64,), (128,), (256,), (512,))
    aspect_ratios = ((0.5, 1.0, 2.0),) * len(anchor_sizes)
    rpn_anchor_generator = AnchorGenerator(
        anchor_sizes, aspect_ratios
    )

对于普通的 FasterRCNN 只需要将 feature_map 输入到 rpn 网络生成 proposals 即可。但是由于加入 FPN，需要将多个 feature_map 逐个输入到 rpn 网络。

图6

接下来看看 AnchorGenerator 具体实现：

class AnchorGenerator(nn.Module):
        ......

    def generate_anchors(self, scales, aspect_ratios, dtype=torch.float32, device="cpu"):
        # type: (List[int], List[float], int, Device)  # noqa: F821
        scales = torch.as_tensor(scales, dtype=dtype, device=device)
        aspect_ratios = torch.as_tensor(aspect_ratios, dtype=dtype, device=device)
        h_ratios = torch.sqrt(aspect_ratios)
        w_ratios = 1 / h_ratios

        ws = (w_ratios[:, None] * scales[None, :]).view(-1)
        hs = (h_ratios[:, None] * scales[None, :]).view(-1)

        base_anchors = torch.stack([-ws, -hs, ws, hs], dim=1) / 2
        return base_anchors.round()

    def set_cell_anchors(self, dtype, device):
        # type: (int, Device) -> None    # noqa: F821
        ......

        cell_anchors = [
            self.generate_anchors(
                sizes,
                aspect_ratios,
                dtype,
                device
            )
            for sizes, aspect_ratios in zip(self.sizes, self.aspect_ratios)
        ]
        self.cell_anchors = cell_anchors

首先，每个位置有 5 种 anchor_size 和 3 种 aspect_ratios，所以每个位置生成 15 个 base_anchors：

[ -23.,  -11.,   23.,   11.]
[ -16.,  -16.,   16.,   16.] # w = h = 32,  ratio = 1
[ -11.,  -23.,   11.,   23.] 
[ -45.,  -23.,   45.,   23.]
[ -32.,  -32.,   32.,   32.] # w = h = 64,  ratio = 1
[ -23.,  -45.,   23.,   45.]
[ -91.,  -45.,   91.,   45.]
[ -64.,  -64.,   64.,   64.] # w = h = 128, ratio = 1
[ -45.,  -91.,   45.,   91.]
[-181.,  -91.,  181.,   91.]
[-128., -128.,  128.,  128.] # w = h = 256, ratio = 1
[ -91., -181.,   91.,  181.]
[-362., -181.,  362.,  181.]
[-256., -256.,  256.,  256.] # w = h = 512, ratio = 1
[-181., -362.,  181.,  362.]

注意 base_anchors 的中心都是点，如下图所示：

图7 base_anchor（此图只画了32/64/128的base_anchor）

接着来看 AnchorGenerator.grid_anchors 函数：

# AnchorGenerator
   def grid_anchors(self, grid_sizes, strides):
        # type: (List[List[int]], List[List[Tensor]])
        anchors = []
        cell_anchors = self.cell_anchors
        assert cell_anchors is not None

        for size, stride, base_anchors in zip(
            grid_sizes, strides, cell_anchors
        ):
            grid_height, grid_width = size
            stride_height, stride_width = stride
            device = base_anchors.device

            # For output anchor, compute [x_center, y_center, x_center, y_center]
            shifts_x = torch.arange(
                0, grid_width, dtype=torch.float32, device=device
            ) * stride_width
            shifts_y = torch.arange(
                0, grid_height, dtype=torch.float32, device=device
            ) * stride_height
            shift_y, shift_x = torch.meshgrid(shifts_y, shifts_x)
            shift_x = shift_x.reshape(-1)
            shift_y = shift_y.reshape(-1)
            shifts = torch.stack((shift_x, shift_y, shift_x, shift_y), dim=1)

            # For every (base anchor, output anchor) pair,
            # offset each zero-centered base anchor by the center of the output anchor.
            anchors.append(
                (shifts.view(-1, 1, 4) + base_anchors.view(1, -1, 4)).reshape(-1, 4)
            )

        return anchors

    def forward(self, image_list, feature_maps):
        # type: (ImageList, List[Tensor])
        grid_sizes = list([feature_map.shape[-2:] for feature_map in feature_maps])
        image_size = image_list.tensors.shape[-2:]
        dtype, device = feature_maps[0].dtype, feature_maps[0].device
        strides = [[torch.tensor(image_size[0] / g[0], dtype=torch.int64, device=device),
                    torch.tensor(image_size[1] / g[1], dtype=torch.int64, device=device)] for g in grid_sizes]
        self.set_cell_anchors(dtype, device)
        anchors_over_all_feature_maps = self.cached_grid_anchors(grid_sizes, strides)
        ......

在之前提到，由于有 FPN 网络，所以输入 rpn 的是多个特征。为了方便介绍，以下都是以某一个特征进行描述，其他特征类似。

假设有的特征，首先会计算这个特征相对于输入图像的下采样倍数 stride：

然后生成一个大小的网格，每个格子长度为 stride，如下图：

# AnchorGenerator.grid_anchors(...)
shifts_x = torch.arange(0, grid_width, dtype=torch.float32, device=device) * stride_width
shifts_y = torch.arange(0, grid_height, dtype=torch.float32, device=device) * stride_height
shift_y, shift_x = torch.meshgrid(shifts_y, shifts_x)

图8

然后将 base_anchors 的中心从移动到网格的点，且在网格的每个点都放置一组 base_anchors。这样就在当前 feature_map 上有了很多的 anchors。

需要特别说明，stride 代表网络的感受野，网络不可能检测到比 feature_map 更密集的框了！所以才只会在网格中每个点设置 anchors（反过来说，如果在网格的两个点之间设置 anchors，那么就对应 feature_map 中半个点，显然不合理）。

# AnchorGenerator.grid_anchors(...)
anchors.append((shifts.view(-1, 1, 4) + base_anchors.view(1, -1, 4)).reshape(-1, 4))

图9 （注：为了方便描述，这里只画了3个anchor，实际每个点有9个anchor）

放置好 anchors 后，接下来就要调整网络，使网络输出能够判断每个 anchor 是否有目标，同时还要有 bounding box regression 需要的4个值。

class RPNHead(nn.Module):
    def __init__(self, in_channels, num_anchors):
        super(RPNHead, self).__init__()
        self.conv = nn.Conv2d(
            in_channels, in_channels, kernel_size=3, stride=1, padding=1
        )
        self.cls_logits = nn.Conv2d(in_channels, num_anchors, kernel_size=1, stride=1)
        self.bbox_pred = nn.Conv2d(
            in_channels, num_anchors * 4, kernel_size=1, stride=1
        )

    def forward(self, x):
        logits = []
        bbox_reg = []
        for feature in x:
            t = F.relu(self.conv(feature))
            logits.append(self.cls_logits(t))
            bbox_reg.append(self.bbox_pred(t))
        return logits, bbox_reg

假设 feature 的大小，每个点个 anchor。从 RPNHead 的代码中可以明显看到：

• 首先进行 3x3 卷积

• 然后对 feature 进行卷积，输出 cls_logits 大小是，对应每个 anchor 是否有目标；

• 同时feature 进行卷积，输出 bbox_pred 大小是，对应每个点的4个框位置回归信息。

# RPNHead.__init__(...)
self.cls_logits = nn.Conv2d(in_channels, num_anchors, kernel_size=1, stride=1)         
self.bbox_pred = nn.Conv2d(in_channels, num_anchors * 4, kernel_size=1, stride=1)

<img data-ratio="0.44166666666666665" data-src="https://mmbiz.qpic.cn/sz_mmbiz_jpg/gYUsOT36vfrbdDSbJSdKPuQ1da5xar141eo0ElS38Vlibicg4hnDW2CqGk7RWqWUibiceEGVpGt4ZEcNxaTMWuATvA/640?wx_fmt=jpeg" data-type="jpeg" data-w="720" style="display: block;max-width: 100%;width: 100%;margin: 0 auto;" />

图10（注：为了方便描述，这里只画了3个anchor，实际每个点有9个anchor）

上述过程只是单个 feature_map 的处理流程。对于 FPN 网络的输出的多个大小不同的 feature_maps，每个特征图都会按照上述过程计算 stride 和网格，并设置 anchors。当处理完后获得密密麻麻的各种 anchors 了。

接下来进入 RegionProposalNetwork 类：

# FasterRCNN.__init__(...)
rpn_pre_nms_top_n = dict(training=rpn_pre_nms_top_n_train, testing=rpn_pre_nms_top_n_test)
rpn_post_nms_top_n = dict(training=rpn_post_nms_top_n_train, testing=rpn_post_nms_top_n_test)

# rpn_anchor_generator 生成anchors
# rpn_head 调整feature_map获得cls_logits+bbox_pred
rpn = RegionProposalNetwork(
    rpn_anchor_generator, rpn_head,
    rpn_fg_iou_thresh, rpn_bg_iou_thresh,
    rpn_batch_size_per_image, rpn_positive_fraction,
    rpn_pre_nms_top_n, rpn_post_nms_top_n, rpn_nms_thresh)

RegionProposalNetwork 类的用是：

• test 阶段 ：计算有目标的 anchor 并进行框回归生成 proposals，然后 NMS

• train 阶段 ：除了上面的作用，还计算 rpn loss

class RegionProposalNetwork(torch.nn.Module):
    .......

    def forward(self, images, features, targets=None):
        features = list(features.values())
        objectness, pred_bbox_deltas = self.head(features)
        anchors = self.anchor_generator(images, features)

        num_images = len(anchors)
        num_anchors_per_level_shape_tensors = [o[0].shape for o in objectness]
        num_anchors_per_level = [s[0] * s[1] * s[2] for s in num_anchors_per_level_shape_tensors]
        objectness, pred_bbox_deltas = \
            concat_box_prediction_layers(objectness, pred_bbox_deltas)
        # apply pred_bbox_deltas to anchors to obtain the decoded proposals
        # note that we detach the deltas because Faster R-CNN do not backprop through
        # the proposals
        proposals = self.box_coder.decode(pred_bbox_deltas.detach(), anchors)
        proposals = proposals.view(num_images, -1, 4)
        boxes, scores = self.filter_proposals(proposals, objectness, images.image_sizes, num_anchors_per_level)

        losses = {}
        if self.training:
            assert targets is not None
            labels, matched_gt_boxes = self.assign_targets_to_anchors(anchors, targets)
            regression_targets = self.box_coder.encode(matched_gt_boxes, anchors)
            loss_objectness, loss_rpn_box_reg = self.compute_loss(
                objectness, pred_bbox_deltas, labels, regression_targets)
            losses = {
                "loss_objectness": loss_objectness,
                "loss_rpn_box_reg": loss_rpn_box_reg,
            }
        return boxes, losses

具体来看，首先计算有目标的 anchor 并进行框回归生成 proposals ：

# RegionProposalNetwork.forward(...)
objectness, pred_bbox_deltas = self.head(features)
anchors = self.anchor_generator(images, features)
......
proposals = self.box_coder.decode(pred_bbox_deltas.detach(), anchors)
proposals = proposals.view(num_images, -1, 4)

然后依照 objectness 置信由大到小度排序（优先提取更可能包含目标的的），并 NMS，生成 boxes （即 NMS 后的 proposal boxes ） ：

# RegionProposalNetwork.forward(...)
boxes, scores = self.filter_proposals(proposals, objectness, images.image_sizes, num_anchors_per_level)

如果是训练阶段，还要将 boxes 与 anchors 进行匹配，计算 cls_logits 的损失 loss_objectness，同时计算 bbox_pred 的损失 loss_rpn_box_reg。

在 RegionProposalNetwork 之后已经生成了 boxes ，接下来就要提取 boxes 内的特征进行 roi_pooling ：

roi_heads = RoIHeads(
    # Box
    box_roi_pool, box_head, box_predictor,
    box_fg_iou_thresh, box_bg_iou_thresh,
    box_batch_size_per_image, box_positive_fraction,
    bbox_reg_weights,
    box_score_thresh, box_nms_thresh, box_detections_per_img)

这里一点问题是如何计算 box 所属的 feature_map：

• 对于原始 FasterRCNN，只在 backbone 的最后一层 feature_map 提取 box 对应特征；

• 当加入 FPN 后 backbone 会输出多个特征图，需要计算当前 boxes 对应于哪一个特征。

如下图：

图11

class MultiScaleRoIAlign(nn.Module):
   ......

   def infer_scale(self, feature, original_size):
        # type: (Tensor, List[int])
        # assumption: the scale is of the form 2 ** (-k), with k integer
        size = feature.shape[-2:]
        possible_scales = torch.jit.annotate(List[float], [])
        for s1, s2 in zip(size, original_size):
            approx_scale = float(s1) / float(s2)
            scale = 2 ** float(torch.tensor(approx_scale).log2().round())
            possible_scales.append(scale)
        assert possible_scales[0] == possible_scales[1]
        return possible_scales[0]

    def setup_scales(self, features, image_shapes):
        # type: (List[Tensor], List[Tuple[int, int]])
        assert len(image_shapes) != 0
        max_x = 0
        max_y = 0
        for shape in image_shapes:
            max_x = max(shape[0], max_x)
            max_y = max(shape[1], max_y)
        original_input_shape = (max_x, max_y)

        scales = [self.infer_scale(feat, original_input_shape) for feat in features]
        # get the levels in the feature map by leveraging the fact that the network always
        # downsamples by a factor of 2 at each level.
        lvl_min = -torch.log2(torch.tensor(scales[0], dtype=torch.float32)).item()
        lvl_max = -torch.log2(torch.tensor(scales[-1], dtype=torch.float32)).item()
        self.scales = scales
        self.map_levels = initLevelMapper(int(lvl_min), int(lvl_max))

首先计算每个 feature_map 相对于网络输入 image 的下采样倍率 scale。其中 infer_scale 函数采用如下的近似公式：

该公式相当于做了一个简单的映射，将不同的 feature_map 与 image 大小比映射到附近的尺度：

图12

例如对于 FasterRCNN 实际值为：

之后设置 lvl_min=2 和 lvl_max=5：

# MultiScaleRoIAlign.setup_scales(...)
# get the levels in the feature map by leveraging the fact that the network always
# downsamples by a factor of 2 at each level.
lvl_min = -torch.log2(torch.tensor(scales[0], dtype=torch.float32)).item()
lvl_max = -torch.log2(torch.tensor(scales[-1], dtype=torch.float32)).item()

接着使用 FPN 原文中的公式计算 box 所在 anchor（其中，为 box 面积）：

class LevelMapper(object)
    def __init__(self, k_min, k_max, canonical_scale=224, canonical_level=4, eps=1e-6):
        self.k_min = k_min          # lvl_min=2
        self.k_max = k_max          # lvl_max=5
        self.s0 = canonical_scale   # 224
        self.lvl0 = canonical_level # 4
        self.eps = eps

    def __call__(self, boxlists):
        s = torch.sqrt(torch.cat([box_area(boxlist) for boxlist in boxlists]))

        # Eqn.(1) in FPN paper
        target_lvls = torch.floor(self.lvl0 + torch.log2(s / self.s0) + torch.tensor(self.eps, dtype=s.dtype))
        target_lvls = torch.clamp(target_lvls, min=self.k_min, max=self.k_max)
        return (target_lvls.to(torch.int64) - self.k_min).to(torch.int64)

其中 torch.clamp(input, min, max) → Tensor 函数的作用是截断，防止越界：

可以看到，通过 LevelMapper 类将不同大小的 box 定位到某个 feature_map，如下图。之后就是按照图11中的流程进行 roi_pooling 操作。

图13

在确定 proposal box 所属 FPN 中哪个 feature_map 之后，接着来看 MultiScaleRoIAlign 如何进行 roi_pooling 操作：

class MultiScaleRoIAlign(nn.Module):
   ......

   def forward(self, x, boxes, image_shapes):
        # type: (Dict[str, Tensor], List[Tensor], List[Tuple[int, int]]) -> Tensor
        x_filtered = []
        for k, v in x.items():
            if k in self.featmap_names:
                x_filtered.append(v)
        num_levels = len(x_filtered)
        rois = self.convert_to_roi_format(boxes)
        if self.scales is None:
            self.setup_scales(x_filtered, image_shapes)

        scales = self.scales
        assert scales is not None

        # 没有 FPN 时，只有1/32的最后一个feature_map进行roi_pooling
        if num_levels == 1:
            return roi_align(
                x_filtered[0], rois,
                output_size=self.output_size,
                spatial_scale=scales[0],
                sampling_ratio=self.sampling_ratio
            )

        # 有 FPN 时，有4个feature_map进行roi_pooling
        # 首先按照
        mapper = self.map_levels
        assert mapper is not None

        levels = mapper(boxes)

        num_rois = len(rois)
        num_channels = x_filtered[0].shape[1]

        dtype, device = x_filtered[0].dtype, x_filtered[0].device
        result = torch.zeros(
            (num_rois, num_channels,) + self.output_size,
            dtype=dtype,
            device=device,
        )

        tracing_results = []
        for level, (per_level_feature, scale) in enumerate(zip(x_filtered, scales)):
            idx_in_level = torch.nonzero(levels == level).squeeze(1)
            rois_per_level = rois[idx_in_level]

            result_idx_in_level = roi_align(
                per_level_feature, rois_per_level,
                output_size=self.output_size,
                spatial_scale=scale, sampling_ratio=self.sampling_ratio)

            if torchvision._is_tracing():
                tracing_results.append(result_idx_in_level.to(dtype))
            else:
                result[idx_in_level] = result_idx_in_level

        if torchvision._is_tracing():
            result = _onnx_merge_levels(levels, tracing_results)

        return result

在 MultiScaleRoIAlign.forward(...) 函数可以看到：

• 没有 FPN 时，只有1/32的最后一个 feature_map 进行 roi_pooling

if num_levels == 1:
            return roi_align(
                x_filtered[0], rois,
                output_size=self.output_size,
                spatial_scale=scales[0],
                sampling_ratio=self.sampling_ratio
            )

• 有 FPN 时，有4个的 feature maps 参加计算。首先计算每个每个 box 所属哪个 feature map ，再在所属 feature map 进行 roi_pooling

# 首先计算每个每个 box 所属哪个 feature map
        levels = mapper(boxes) 
        ......

        # 再在所属  feature map 进行 roi_pooling
        # 即 idx_in_level = torch.nonzero(levels == level).squeeze(1)
        for level, (per_level_feature, scale) in enumerate(zip(x_filtered, scales)):
            idx_in_level = torch.nonzero(levels == level).squeeze(1)
            rois_per_level = rois[idx_in_level]

            result_idx_in_level = roi_align(
                per_level_feature, rois_per_level,
                output_size=self.output_size,
                spatial_scale=scale, sampling_ratio=self.sampling_ratio)

之后就获得了所谓的 7x7 特征（在 FasterRCNN.__init__(...) 中设置了 output_size=7）。需要说明，原始 FasterRCNN 应该是使用 roi_pooling，但是这里使用 roi_align 代替以提升检测器性能。

对于 torchvision.ops.roi_align 函数输入的参数，分别为：

• per_level_feature 代表 FPN 输出的某一 feature_map

• rois_per_level 为该特征 feature_map 对应的所有 proposal boxes（之前计算 level得到）

• output_size=7 代表输出为 7x7

• spatial_scale 代表特征 feature_map 相对输入 image 的下采样尺度（如 1/4，1/8，...）

• sampling_ratio 为 roi_align 采样率，有兴趣的读者请自行查阅 MaskRCNN 文章

接下来就是将特征转为最后针对 box 的类别信息（如人、猫、狗、车）和进一步的框回归信息。

class TwoMLPHead(nn.Module):

    def __init__(self, in_channels, representation_size):
        super(TwoMLPHead, self).__init__()

        self.fc6 = nn.Linear(in_channels, representation_size)
        self.fc7 = nn.Linear(representation_size, representation_size)

    def forward(self, x):
        x = x.flatten(start_dim=1)

        x = F.relu(self.fc6(x))
        x = F.relu(self.fc7(x))

        return x


class FastRCNNPredictor(nn.Module):

    def __init__(self, in_channels, num_classes):
        super(FastRCNNPredictor, self).__init__()
        self.cls_score = nn.Linear(in_channels, num_classes)
        self.bbox_pred = nn.Linear(in_channels, num_classes * 4)

    def forward(self, x):
        if x.dim() == 4:
            assert list(x.shape[2:]) == [1, 1]
        x = x.flatten(start_dim=1)
        scores = self.cls_score(x)
        bbox_deltas = self.bbox_pred(x)

        return scores, bbox_deltas

首先 TwoMLPHead 将 7x7 特征经过两个全连接层转为 1024，然后 FastRCNNPredictor 将每个 box 对应的 1024 维特征转为 cls_score 和 bbox_pred :

图14

显然 cls_score 后接 softmax 即为类别概率，可以确定 box 的类别；在确定类别后，在 bbox_pred 中对应类别的4个值即为第二次 bounding box regression 需要的4个偏移值。

简单的说，带有FPN的FasterRCNN网络结构可以用下图表示：

图15

关于训练

FasterRCNN模型在两处地方有损失函数：

• 在 RegionProposalNetwork 类，需要判别 anchor 中是否包含目标从而生成 proposals，这里需要计算 loss

• 在 RoIHeads 类，对 roi_pooling 后的全连接生成的 cls_score 和 bbox_pred 进行训练，也需要计算 loss

首先来看 RegionProposalNetwork 类中的 assign_targets_to_anchors 函数。

def assign_targets_to_anchors(self, anchors, targets):
    # type: (List[Tensor], List[Dict[str, Tensor]])
    labels = []
    matched_gt_boxes = []
    for anchors_per_image, targets_per_image in zip(anchors, targets):
        gt_boxes = targets_per_image["boxes"]

        if gt_boxes.numel() == 0:
            # Background image (negative example)
            device = anchors_per_image.device
            matched_gt_boxes_per_image = torch.zeros(anchors_per_image.shape, dtype=torch.float32, device=device)
            labels_per_image = torch.zeros((anchors_per_image.shape[0],), dtype=torch.float32, device=device)
        else:
            match_quality_matrix = box_ops.box_iou(gt_boxes, anchors_per_image)
            matched_idxs = self.proposal_matcher(match_quality_matrix)
            # get the targets corresponding GT for each proposal
            # NB: need to clamp the indices because we can have a single
            # GT in the image, and matched_idxs can be -2, which goes
            # out of bounds
            matched_gt_boxes_per_image = gt_boxes[matched_idxs.clamp(min=0)]

            labels_per_image = matched_idxs >= 0
            labels_per_image = labels_per_image.to(dtype=torch.float32)
            # Background (negative examples)
            bg_indices = matched_idxs == self.proposal_matcher.BELOW_LOW_THRESHOLD
            labels_per_image[bg_indices] = torch.tensor(0.0)

            # discard indices that are between thresholds
            inds_to_discard = matched_idxs == self.proposal_matcher.BETWEEN_THRESHOLDS
            labels_per_image[inds_to_discard] = torch.tensor(-1.0)

        labels.append(labels_per_image)
        matched_gt_boxes.append(matched_gt_boxes_per_image)
    return labels, matched_gt_boxes

当图像中没有 gt_boxes 时，设置所有 anchor 都为 background（即 label 为 0）：

if gt_boxes.numel() == 0
    # Background image (negative example)
    device = anchors_per_image.device
    matched_gt_boxes_per_image = torch.zeros(anchors_per_image.shape, dtype=torch.float32, device=device)
    labels_per_image = torch.zeros((anchors_per_image.shape[0],), dtype=torch.float32, device=device)

当图像中有 gt_boxes 时，计算 anchor 与 gt_box 的 IOU：

• 选择 IOU < 0.3 的 anchor 为 background，标签为 0

labels_per_image[bg_indices] = torch.tensor(0.0)

• 选择 IOU > 0.7 的 anchor 为 foreground，标签为 1

labels_per_image = matched_idxs >= 0

• 忽略 0.3 < IOU < 0.7 的 anchor，不参与训练

从 FasterRCNN 类的 __init__ 函数默认参数就可以清晰的看到这一点：

rpn_fg_iou_thresh=0.7, rpn_bg_iou_thresh=0.3,

接着来看 RoIHeads 类中的 assign_targets_to_proposals 函数。

def assign_targets_to_proposals(self, proposals, gt_boxes, gt_labels):
    # type: (List[Tensor], List[Tensor], List[Tensor])
    matched_idxs = []
    labels = []
    for proposals_in_image, gt_boxes_in_image, gt_labels_in_image in zip(proposals, gt_boxes, gt_labels):

        if gt_boxes_in_image.numel() == 0:
            # Background image
            device = proposals_in_image.device
            clamped_matched_idxs_in_image = torch.zeros(
                (proposals_in_image.shape[0],), dtype=torch.int64, device=device
            )
            labels_in_image = torch.zeros(
                (proposals_in_image.shape[0],), dtype=torch.int64, device=device
            )
        else:
            #  set to self.box_similarity when https://github.com/pytorch/pytorch/issues/27495 lands
            match_quality_matrix = box_ops.box_iou(gt_boxes_in_image, proposals_in_image)
            matched_idxs_in_image = self.proposal_matcher(match_quality_matrix)

            clamped_matched_idxs_in_image = matched_idxs_in_image.clamp(min=0)

            labels_in_image = gt_labels_in_image[clamped_matched_idxs_in_image]
            labels_in_image = labels_in_image.to(dtype=torch.int64)

            # Label background (below the low threshold)
            bg_inds = matched_idxs_in_image == self.proposal_matcher.BELOW_LOW_THRESHOLD
            labels_in_image[bg_inds] = torch.tensor(0)

            # Label ignore proposals (between low and high thresholds)
            ignore_inds = matched_idxs_in_image == self.proposal_matcher.BETWEEN_THRESHOLDS
            labels_in_image[ignore_inds] = torch.tensor(-1)  # -1 is ignored by sampler

        matched_idxs.append(clamped_matched_idxs_in_image)
        labels.append(labels_in_image)
    return matched_idxs, labels

与 assign_targets_to_anchors 不同，该函数设置：

box_fg_iou_thresh=0.5, box_bg_iou_thresh=0.5,

• IOU > 0.5 的 proposal 为 foreground，标签为对应的 class_id

labels_in_image = gt_labels_in_image[clamped_matched_idxs_in_image]

这里与上面不同：RegionProposalNetwork 只需要判断 anchor 是否有目标，正类别为1；RoIHeads 需要判断 proposal 的具体类别，所以正类别为具体的 class_id。

• IOU < 0.5 的为 background，标签为 0

labels_in_image[bg_inds] = torch.tensor(0)

写在最后

本文简要的介绍了 torchvision 中的 FasterRCNN 实现，并分析我认为重要的知识点。写这篇文章的目的是为阅读代码困难的小伙伴做个指引，鼓励入门新手能够多看看代码实现。若要真正的理解模型（不被面试官问住），要是要看代码！

创作不易，不想被白嫖，求点赞、关注、收藏（作者）三连！