矩阵计算代码: np.meshgrid & DeformConv2d

meshgrid

import numpy as np

X = np.arange(1, 4)
Y = np.arange(11, 13)
# MX.shape=MY.shape=(len(Y), len(X))=(H,W)
MX, MY = np.meshgrid(X, Y)
print(MX)
print(MY)
MP = np.stack([MX, MY], axis=-1)
           

[[1 2 3]
 [1 2 3]]
[[11 11 11]
 [12 12 12]]
           

MP:
	(x0, y0) (x1, y0) (x2, y0)
	(x0, y1) (x1, y1) (x2, y1)
=>
MX:
	x0 x1 x2
	x0 x1 x2
MY:
	y0 y0 y0
	y1 y1 y1
           

mmcv.ops.DeformConv2d

class DeformConv2d(nn.Module):
    ...
    def forward(self, x: Tensor, offset: Tensor) -> Tensor:
        """Deformable Convolutional forward function.

        Args:
            x (Tensor): Input feature, shape (B, C_in, H_in, W_in)
            offset (Tensor): Offset for deformable convolution, shape
                (B, deform_groups*kernel_size[0]*kernel_size[1]*2，
                H_out, W_out), H_out, W_out are equal to the output's.

                An offset is like `[y0, x0, y1, x1, y2, x2, ..., y8, x8]`.
                The spatial arrangement is like:

                .. code:: text

                    (x0, y0) (x1, y1) (x2, y2)
                    (x3, y3) (x4, y4) (x5, y5)
                    (x6, y6) (x7, y7) (x8, y8)

        Returns:
            Tensor: Output of the layer.
        """
           

可知offset是先行优先排列展开的点集合，再y优先的展开为一维向量。

在RepPointsHead中对feat_map上每个特征点预测的pts，都是相对中心点的偏移，而DeformaConv2D中的offset是相对卷积kernel上对应点的。

dcn_kernel = 3
dcn_pad = dcn_kernel // 2  # dcn_stride=1, dcn_kernel is odd number
base_off = np.arange(-dcn_pad, dcn_pad+1)
base_off_x, base_off_y = np.meshgrid(base_off, base_off)
base_off = np.stack([base_off_y , base_off_x], axis=-1).reshape(-1)
print(base_off)
base_off = torch.tensor(base_off).view(1, -1, 1, 1)

dcn_off = pts_out_init - base_off
feat = dconv(feat, dcn_off.type_as(feat))
           

array([-1, -1, -1,  0, -1,  1,  0, -1,  0,  0,  0,  1,  1, -1,  1,  0,  1, 1])