精确分割拓扑管状结构例如血管和道路，对医疗各个领域至关重要，可确保下游任务的准确性和效率。然而许多因素使分割任务变得复杂，包括细小脆弱的局部结构和复杂多变的全局形态。针对这个问题，作者提出了动态蛇卷积，该结构在管状分割任务上获得了极好的性能。

论文：Dynamic Snake Convolution based on Topological Geometric Constraints for Tubular Structure Segmentation

中文论文：拓扑几何约束管状结构分割的动态蛇卷积

代码：https://github.com/yaoleiqi/dscnet

一、适用场景

管状目标分割的特点是细长且复杂，标准卷积、空洞卷积无法更具目标特征调整关注区域，可变形卷积可以更具特征自适应学习感兴趣区域，但是对于管状目标，可变形卷积无法限制关注区域的连通性，而动态蛇卷积限制了关注区域的连通性，是的其更适合管状场景。

二、动态蛇卷积

对于一个标准3x3的2D卷积核K，其表示为：

为了赋予卷积核更多灵活性，使其能够聚焦于目标 的复杂几何特征，受到可变形卷积的启发，引入了变形偏 移 ∆。然而，如果模型被完全自由地学习变形偏移，感知场往往会偏离目标，特别是在处理细长管状结构的情 况下。因此，作者采用了一个迭代策略（下图），依次选 择每个要处理的目标的下一个位置进行观察，从而确保关注的连续性，不会由于大的变形偏移而将感知范围扩 散得太远。

在动态蛇形卷积中，作者将标准卷积核在 x 轴和 y 轴方向都进行了直线化。考虑一个大小为 9 的卷积 核，以 x 轴方向为例，K 中每个网格的具体位置表示 为：Ki±c = (xi±c, yi±c)，其中 c = 0, 1, 2, 3, 4 表示距离 中心网格的水平距离。卷积核 K 中每个网格位置 Ki±c 的选择是一个累积过程。从中心位置 Ki 开始，远离中 心网格的位置取决于前一个网格的位置：Ki+1 相对于 Ki 增加了偏移量 ∆ = {δ|δ ∈ [−1, 1]}。因此，偏移量 需要进行累加 Σ，从而确保卷积核符合线性形态结构。 上图中 x 轴方向的变化为：

y轴方向的变化为：

由于偏移量 ∆ 通常是小数，然而坐标通常是整数 形式，因此采用双线性插值，表示为：

其中，K 表示方程 2和方程 3的小数位置，K′ 列 举所有整数空间位置，B 是双线性插值核，可以分解为 两个一维核，即：

再给个整体图：

三、代码

蛇卷积的代码如下：

# -*- coding: utf-8 -*-
import os
import torch
from torch import nn
import einops"""Dynamic Snake Convolution Module"""class DSConv_pro(nn.Module):def __init__(self,in_channels: int = 1,out_channels: int = 1,kernel_size: int = 9,extend_scope: float = 1.0,morph: int = 0,if_offset: bool = True,device: str | torch.device = "cuda",):"""A Dynamic Snake Convolution ImplementationBased on:TODOArgs:in_ch: number of input channels. Defaults to 1.out_ch: number of output channels. Defaults to 1.kernel_size: the size of kernel. Defaults to 9.extend_scope: the range to expand. Defaults to 1 for this method.morph: the morphology of the convolution kernel is mainly divided into two types along the x-axis (0) and the y-axis (1) (see the paper for details).if_offset: whether deformation is required,  if it is False, it is the standard convolution kernel. Defaults to True."""super().__init__()if morph not in (0, 1):raise ValueError("morph should be 0 or 1.")self.kernel_size = kernel_sizeself.extend_scope = extend_scopeself.morph = morphself.if_offset = if_offsetself.device = torch.device(device)self.to(device)# self.bn = nn.BatchNorm2d(2 * kernel_size)self.gn_offset = nn.GroupNorm(kernel_size, 2 * kernel_size)self.gn = nn.GroupNorm(out_channels // 4, out_channels)self.relu = nn.ReLU(inplace=True)self.tanh = nn.Tanh()self.offset_conv = nn.Conv2d(in_channels, 2 * kernel_size, 3, padding=1)self.dsc_conv_x = nn.Conv2d(in_channels,out_channels,kernel_size=(kernel_size, 1),stride=(kernel_size, 1),padding=0,)self.dsc_conv_y = nn.Conv2d(in_channels,out_channels,kernel_size=(1, kernel_size),stride=(1, kernel_size),padding=0,)def forward(self, input: torch.Tensor):# Predict offset map between [-1, 1]offset = self.offset_conv(input)# offset = self.bn(offset)offset = self.gn_offset(offset)offset = self.tanh(offset)# Run deformative convy_coordinate_map, x_coordinate_map = get_coordinate_map_2D(offset=offset,morph=self.morph,extend_scope=self.extend_scope,device=self.device,)deformed_feature = get_interpolated_feature(input,y_coordinate_map,x_coordinate_map,)if self.morph == 0:output = self.dsc_conv_x(deformed_feature)elif self.morph == 1:output = self.dsc_conv_y(deformed_feature)# Groupnorm & ReLUoutput = self.gn(output)output = self.relu(output)return outputdef get_coordinate_map_2D(offset: torch.Tensor,morph: int,extend_scope: float = 1.0,device: str | torch.device = "cuda",
):"""Computing 2D coordinate map of DSCNet based on: TODOArgs:offset: offset predict by network with shape [B, 2*K, W, H]. Here K refers to kernel size.morph: the morphology of the convolution kernel is mainly divided into two types along the x-axis (0) and the y-axis (1) (see the paper for details).extend_scope: the range to expand. Defaults to 1 for this method.device: location of data. Defaults to 'cuda'.Return:y_coordinate_map: coordinate map along y-axis with shape [B, K_H * H, K_W * W]x_coordinate_map: coordinate map along x-axis with shape [B, K_H * H, K_W * W]"""if morph not in (0, 1):raise ValueError("morph should be 0 or 1.")batch_size, _, width, height = offset.shapekernel_size = offset.shape[1] // 2center = kernel_size // 2device = torch.device(device)y_offset_, x_offset_ = torch.split(offset, kernel_size, dim=1)y_center_ = torch.arange(0, width, dtype=torch.float32, device=device)y_center_ = einops.repeat(y_center_, "w -> k w h", k=kernel_size, h=height)x_center_ = torch.arange(0, height, dtype=torch.float32, device=device)x_center_ = einops.repeat(x_center_, "h -> k w h", k=kernel_size, w=width)if morph == 0:"""Initialize the kernel and flatten the kernely: only need 0x: -num_points//2 ~ num_points//2 (Determined by the kernel size)"""y_spread_ = torch.zeros([kernel_size], device=device)x_spread_ = torch.linspace(-center, center, kernel_size, device=device)y_grid_ = einops.repeat(y_spread_, "k -> k w h", w=width, h=height)x_grid_ = einops.repeat(x_spread_, "k -> k w h", w=width, h=height)y_new_ = y_center_ + y_grid_x_new_ = x_center_ + x_grid_y_new_ = einops.repeat(y_new_, "k w h -> b k w h", b=batch_size)x_new_ = einops.repeat(x_new_, "k w h -> b k w h", b=batch_size)y_offset_ = einops.rearrange(y_offset_, "b k w h -> k b w h")y_offset_new_ = y_offset_.detach().clone()# The center position remains unchanged and the rest of the positions begin to swing# This part is quite simple. The main idea is that "offset is an iterative process"y_offset_new_[center] = 0for index in range(1, center + 1):y_offset_new_[center + index] = (y_offset_new_[center + index - 1] + y_offset_[center + index])y_offset_new_[center - index] = (y_offset_new_[center - index + 1] + y_offset_[center - index])y_offset_new_ = einops.rearrange(y_offset_new_, "k b w h -> b k w h")y_new_ = y_new_.add(y_offset_new_.mul(extend_scope))y_coordinate_map = einops.rearrange(y_new_, "b k w h -> b (w k) h")x_coordinate_map = einops.rearrange(x_new_, "b k w h -> b (w k) h")elif morph == 1:"""Initialize the kernel and flatten the kernely: -num_points//2 ~ num_points//2 (Determined by the kernel size)x: only need 0"""y_spread_ = torch.linspace(-center, center, kernel_size, device=device)x_spread_ = torch.zeros([kernel_size], device=device)y_grid_ = einops.repeat(y_spread_, "k -> k w h", w=width, h=height)x_grid_ = einops.repeat(x_spread_, "k -> k w h", w=width, h=height)y_new_ = y_center_ + y_grid_x_new_ = x_center_ + x_grid_y_new_ = einops.repeat(y_new_, "k w h -> b k w h", b=batch_size)x_new_ = einops.repeat(x_new_, "k w h -> b k w h", b=batch_size)x_offset_ = einops.rearrange(x_offset_, "b k w h -> k b w h")x_offset_new_ = x_offset_.detach().clone()# The center position remains unchanged and the rest of the positions begin to swing# This part is quite simple. The main idea is that "offset is an iterative process"x_offset_new_[center] = 0for index in range(1, center + 1):x_offset_new_[center + index] = (x_offset_new_[center + index - 1] + x_offset_[center + index])x_offset_new_[center - index] = (x_offset_new_[center - index + 1] + x_offset_[center - index])x_offset_new_ = einops.rearrange(x_offset_new_, "k b w h -> b k w h")x_new_ = x_new_.add(x_offset_new_.mul(extend_scope))y_coordinate_map = einops.rearrange(y_new_, "b k w h -> b w (h k)")x_coordinate_map = einops.rearrange(x_new_, "b k w h -> b w (h k)")return y_coordinate_map, x_coordinate_mapdef get_interpolated_feature(input_feature: torch.Tensor,y_coordinate_map: torch.Tensor,x_coordinate_map: torch.Tensor,interpolate_mode: str = "bilinear",
):"""From coordinate map interpolate feature of DSCNet based on: TODOArgs:input_feature: feature that to be interpolated with shape [B, C, H, W]y_coordinate_map: coordinate map along y-axis with shape [B, K_H * H, K_W * W]x_coordinate_map: coordinate map along x-axis with shape [B, K_H * H, K_W * W]interpolate_mode: the arg 'mode' of nn.functional.grid_sample, can be 'bilinear' or 'bicubic' . Defaults to 'bilinear'.Return:interpolated_feature: interpolated feature with shape [B, C, K_H * H, K_W * W]"""if interpolate_mode not in ("bilinear", "bicubic"):raise ValueError("interpolate_mode should be 'bilinear' or 'bicubic'.")y_max = input_feature.shape[-2] - 1x_max = input_feature.shape[-1] - 1y_coordinate_map_ = _coordinate_map_scaling(y_coordinate_map, origin=[0, y_max])x_coordinate_map_ = _coordinate_map_scaling(x_coordinate_map, origin=[0, x_max])y_coordinate_map_ = torch.unsqueeze(y_coordinate_map_, dim=-1)x_coordinate_map_ = torch.unsqueeze(x_coordinate_map_, dim=-1)# Note here grid with shape [B, H, W, 2]# Where [:, :, :, 2] refers to [x ,y]grid = torch.cat([x_coordinate_map_, y_coordinate_map_], dim=-1)interpolated_feature = nn.functional.grid_sample(input=input_feature,grid=grid,mode=interpolate_mode,padding_mode="zeros",align_corners=True,)return interpolated_featuredef _coordinate_map_scaling(coordinate_map: torch.Tensor,origin: list,target: list = [-1, 1],
):"""Map the value of coordinate_map from origin=[min, max] to target=[a,b] for DSCNet based on: TODOArgs:coordinate_map: the coordinate map to be scaledorigin: original value range of coordinate map, e.g. [coordinate_map.min(), coordinate_map.max()]target: target value range of coordinate map,Defaults to [-1, 1]Return:coordinate_map_scaled: the coordinate map after scaling"""min, max = origina, b = targetcoordinate_map_scaled = torch.clamp(coordinate_map, min, max)scale_factor = (b - a) / (max - min)coordinate_map_scaled = a + scale_factor * (coordinate_map_scaled - min)return coordinate_map_scaled