yolov3损失函数分析_def build_targets(pred_boxes, pred_cls, target, an

代码下载：https://github.com/pakaqiu/yolov3_simple
视频链接：https://www.bilibili.com/video/BV1MK4y1X74Q?p=1
yolov1到v3损失函数都是逐步修改而来，特别是v4，v5损失函数的改动对于目标检测的性能和效果具有较大的提升；当然v3相比v1，v2还是有不少提升的，这种性能提升不仅仅是损失函数所带来的，网络结构的修改和优化也具有比较可观的效果。本文主要讲解v3损失函数的设计，这里首先回顾下v1，v2：
v1损失函数：

v2的损失函数：
v2只是在v1的基础上改动了box宽高的损失计算方式，即去除了w和h的根号：

v3相对v2最大的改动就是分类的损失以及box置信度的损失改为了二分交叉熵：

上式中S为网络输出层网格的数目，B为anchors的数目；网络的输出为SS大小的特征图，即网格SS；每个网格有B个anchor，一共会得到SSB个bounding box，那这么多个bounding box，损失函数是如何进行回归的呢？下面对v3的损失函数中的(a)-(e)一一进行解析：
$I_{ij}^{obj}$表示第i个网格中第j个anchor，如果第j个anchor负责这个object，那么$I_{ij}^{obj}=1$，否则的话就等于0。一个网络中有B个anchor，那么负责就是B个anchor中与ground truth box的IOU最大的那个anchor。
$I_{ij}^{noobj}$表示第i个网格中的第j个anchor不负责这个object。

上面Loss中的(a)表示目标物体的中心坐标的误差，在训练过程中回归的是是中心坐标的偏移量，这里需要结合代码去仔细体会；每个网格有B个anchors，在训练过程中只取iou最大的anchor才能负责当前网格的回归。
Loss中的(b)表示目标物体的宽高坐标误差，训练过程中并不是直接回归目标物体的宽高坐标，而是利用网格本身满足条件的最佳anchor去回归宽高坐标误差的。
Loss中 ( c) ，(d)表示目标物体置信度的误差，这里的损失是采用交叉熵来进行计算的，此外，不管网格是否有负责某个目标物体，都会计算置信度误差，但是输入的图像中大部分的空间不包含目标物体，只有少部分空间包含了目标物体，因此需要添加权重对不包含目标物体的置信度损失进行约束。其中${\tilde{C}}_j^i$表示真实值，${\tilde{C}}_j^i$的值由网格的bounding box是否负责预测某个对象决定；负责，则${\tilde{C}}_j^i$ = 1，反之，则相反；$C_j^i$表示拟合值。
Loss中(e)表示目标物体的分类误差，这里的损失采用交叉熵进行计算，只有当第i个网格的第j个anchor负责某个真实目标物体，这个anchor产生的bounding box才会去计算分类损失精度。
具体代码实现：

    def forward(self, x, targets=None, img_dim=None):

        # Tensors for cuda support
        FloatTensor = torch.cuda.FloatTensor if x.is_cuda else torch.FloatTensor
        LongTensor = torch.cuda.LongTensor if x.is_cuda else torch.LongTensor
        ByteTensor = torch.cuda.ByteTensor if x.is_cuda else torch.ByteTensor

        self.img_dim = img_dim
        num_samples = x.size(0)
        grid_size = x.size(2)

        prediction = (
            x.view(num_samples, self.num_anchors, self.num_classes + 5, grid_size, grid_size)
            .permute(0, 1, 3, 4, 2)
            .contiguous()
        )

        # Get outputs
        x = torch.sigmoid(prediction[..., 0])  # Center x
        y = torch.sigmoid(prediction[..., 1])  # Center y
        w = prediction[..., 2]  # Width
        h = prediction[..., 3]  # Height
        pred_conf = torch.sigmoid(prediction[..., 4])  # Conf
        pred_cls = torch.sigmoid(prediction[..., 5:])  # Cls pred.

        # If grid size does not match current we compute new offsets
        if grid_size != self.grid_size:
            self.compute_grid_offsets(grid_size, cuda=x.is_cuda)

        # Add offset and scale with anchors
        pred_boxes = FloatTensor(prediction[..., :4].shape)
        pred_boxes[..., 0] = x.data + self.grid_x
        pred_boxes[..., 1] = y.data + self.grid_y
        pred_boxes[..., 2] = torch.exp(w.data) * self.anchor_w
        pred_boxes[..., 3] = torch.exp(h.data) * self.anchor_h

        output = torch.cat(
            (
                pred_boxes.view(num_samples, -1, 4) * self.stride,
                pred_conf.view(num_samples, -1, 1),
                pred_cls.view(num_samples, -1, self.num_classes),
            ),
            -1,
        )

        if targets is None:
            return output, 0
        else:
            iou_scores, class_mask, obj_mask, noobj_mask, tx, ty, tw, th, tcls, tconf = build_targets(
                pred_boxes=pred_boxes,
                pred_cls=pred_cls,
                target=targets,
                anchors=self.scaled_anchors,
                ignore_thres=self.ignore_thres,
            )

            # Loss : Mask outputs to ignore non-existing objects (except with conf. loss)
            loss_x = self.mse_loss(x[obj_mask], tx[obj_mask])
            loss_y = self.mse_loss(y[obj_mask], ty[obj_mask])
            loss_w = self.mse_loss(w[obj_mask], tw[obj_mask])
            loss_h = self.mse_loss(h[obj_mask], th[obj_mask])
            loss_conf_obj = self.bce_loss(pred_conf[obj_mask], tconf[obj_mask])
            loss_conf_noobj = self.bce_loss(pred_conf[noobj_mask], tconf[noobj_mask])
            loss_conf = self.obj_scale * loss_conf_obj + self.noobj_scale * loss_conf_noobj
            loss_cls = self.bce_loss(pred_cls[obj_mask], tcls[obj_mask])
            total_loss = loss_x + loss_y + loss_w + loss_h + loss_conf + loss_cls

            # Metrics
            cls_acc = 100 * class_mask[obj_mask].mean()
            conf_obj = pred_conf[obj_mask].mean()
            conf_noobj = pred_conf[noobj_mask].mean()
            conf50 = (pred_conf > 0.5).float()
            iou50 = (iou_scores > 0.5).float()
            iou75 = (iou_scores > 0.75).float()
            detected_mask = conf50 * class_mask * tconf
            precision = torch.sum(iou50 * detected_mask) / (conf50.sum() + 1e-16)
            recall50 = torch.sum(iou50 * detected_mask) / (obj_mask.sum() + 1e-16)
            recall75 = torch.sum(iou75 * detected_mask) / (obj_mask.sum() + 1e-16)

            self.metrics = {
                "loss": to_cpu(total_loss).item(),
                "x": to_cpu(loss_x).item(),
                "y": to_cpu(loss_y).item(),
                "w": to_cpu(loss_w).item(),
                "h": to_cpu(loss_h).item(),
                "conf": to_cpu(loss_conf).item(),
                "cls": to_cpu(loss_cls).item(),
                "cls_acc": to_cpu(cls_acc).item(),
                "recall50": to_cpu(recall50).item(),
                "recall75": to_cpu(recall75).item(),
                "precision": to_cpu(precision).item(),
                "conf_obj": to_cpu(conf_obj).item(),
                "conf_noobj": to_cpu(conf_noobj).item(),
                "grid_size": grid_size,
            }

            return output, total_loss
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def build_targets(pred_boxes, pred_cls, target, anchors, ignore_thres):

    ByteTensor = torch.cuda.ByteTensor if pred_boxes.is_cuda else torch.ByteTensor
    FloatTensor = torch.cuda.FloatTensor if pred_boxes.is_cuda else torch.FloatTensor

    nB = pred_boxes.size(0)
    nA = pred_boxes.size(1)
    nC = pred_cls.size(-1)
    nG = pred_boxes.size(2)

    # Output tensors
    obj_mask = ByteTensor(nB, nA, nG, nG).fill_(0)
    noobj_mask = ByteTensor(nB, nA, nG, nG).fill_(1)
    class_mask = FloatTensor(nB, nA, nG, nG).fill_(0)
    iou_scores = FloatTensor(nB, nA, nG, nG).fill_(0)
    tx = FloatTensor(nB, nA, nG, nG).fill_(0)
    ty = FloatTensor(nB, nA, nG, nG).fill_(0)
    tw = FloatTensor(nB, nA, nG, nG).fill_(0)
    th = FloatTensor(nB, nA, nG, nG).fill_(0)
    tcls = FloatTensor(nB, nA, nG, nG, nC).fill_(0)

    # Convert to position relative to box
    target_boxes = target[:, 2:6] * nG
    gxy = target_boxes[:, :2]
    gwh = target_boxes[:, 2:]
    # Get anchors with best iou
    ious = torch.stack([bbox_wh_iou(anchor, gwh) for anchor in anchors])
    best_ious, best_n = ious.max(0) #求最大iou
    # Separate target values
    b, target_labels = target[:, :2].long().t()
    gx, gy = gxy.t()
    gw, gh = gwh.t()
    gi, gj = gxy.long().t()
    # Set masks
    obj_mask[b, best_n, gj, gi] = 1  #最佳anchor对应的位置obj_mask设置为1
    noobj_mask[b, best_n, gj, gi] = 0  #最佳anchor对应位置noobj_mask设置为0

    # Set noobj mask to zero where iou exceeds ignore threshold
    for i, anchor_ious in enumerate(ious.t()):
        noobj_mask[b[i], anchor_ious > ignore_thres, gj[i], gi[i]] = 0  #anchor与gt的iou > ignore_thres的noobj_mask设置为0，即满足该条件的anchor不管

    # Coordinates
    tx[b, best_n, gj, gi] = gx - gx.floor() #中心坐标转换为偏移量
    ty[b, best_n, gj, gi] = gy - gy.floor()
    # Width and height
    tw[b, best_n, gj, gi] = torch.log(gw / anchors[best_n][:, 0] + 1e-16)  #目标物体宽高转换
    th[b, best_n, gj, gi] = torch.log(gh / anchors[best_n][:, 1] + 1e-16)
    # One-hot encoding of label
    tcls[b, best_n, gj, gi, target_labels] = 1
    # Compute label correctness and iou at best anchor
    class_mask[b, best_n, gj, gi] = (pred_cls[b, best_n, gj, gi].argmax(-1) == target_labels).float()
    iou_scores[b, best_n, gj, gi] = bbox_iou(pred_boxes[b, best_n, gj, gi], target_boxes, x1y1x2y2=False)

    tconf = obj_mask.float()
    return iou_scores, class_mask, obj_mask, noobj_mask, tx, ty, tw, th, tcls, tconf
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水平有限，不当之处请指教，谢谢！