function [one_feat_sps, weight_pool_info]=do_sp_pooling(one_feat_img, one_sp_info) img_size=size(one_feat_img); num_units=img_size(1)*img_size(2); dim=img_size(3); one_feat_img=reshape(one_feat_img, [num_units dim]); img_size_org=one_sp_info.img_size; pixel_ind_map=reshape([1: num_units], [img_size(1) img_size(2)]); pixel_ind_map_org=imresize(pixel_ind_map, img_size_org, 'nearest'); pixel_ind_sps=one_sp_info.pixel_ind_sps; num_sp=numel(pixel_ind_sps); weight_pool_info=zeros([num_sp, num_units], 'like', one_feat_img); for idx_sp=1:num_sp pixel_ind_sp_one=pixel_ind_sps{idx_sp}; ind_pixels_in_map=pixel_ind_map_org(pixel_ind_sp_one); [ind_units,~,uniqueIndex] = unique(ind_pixels_in_map); frequency = accumarray(uniqueIndex(:),1)./numel(ind_pixels_in_map); frequency=single(frequency); freq_one_sp=zeros(1, num_units, 'single'); freq_one_sp(ind_units)=frequency; weight_pool_info(idx_sp, :)=freq_one_sp; end one_feat_sps=weight_pool_info*one_feat_img; end， 根据上述代码归纳出所有公式

根据上述代码，可以得到超像素池化的公式如下：

1. 将输入的特征图$\mathbf{X}\in\mathbb{R}^{H\times W\times D}$重塑为$\mathbf{X}'\in\mathbb{R}^{HW\times D}$。

2. 对于每个超像素$\mathbf{S}_i$，找到其包含的像素坐标集合$\mathcal{P}_i$，计算每个像素在超像素中的权重：

$$w_{ij}=\begin{cases} \frac{1}{|\mathcal{P}_i|}, & i\in\mathcal{P}_i \\ 0, & \text{otherwise} \end{cases}$$

其中，$j$表示输入特征图中的像素索引。

3. 将每个超像素的权重向量$\mathbf{w}_i\in\mathbb{R}^{HW}$与输入特征图$\mathbf{X}'$相乘，得到超像素池化后的特征向量$\mathbf{s}_i\in\mathbb{R}^D$：

$$\mathbf{s}_i=\mathbf{w}_i\mathbf{X}'$$

4. 将所有的超像素池化后的特征向量$\mathbf{s}_i$按行堆叠，得到输出的特征图$\mathbf{Y}\in\mathbb{R}^{N\times D}$，其中$N$为超像素的数量。

相关问题

function [one_feat_sps, weight_pool_info]=do_sp_pooling(one_feat_img, one_sp_info) img_size=size(one_feat_img); num_units=img_size(1)*img_size(2); dim=img_size(3); one_feat_img=reshape(one_feat_img, [num_units dim]); img_size_org=one_sp_info.img_size; pixel_ind_map=reshape([1: num_units], [img_size(1) img_size(2)]); pixel_ind_map_org=imresize(pixel_ind_map, img_size_org, 'nearest'); pixel_ind_sps=one_sp_info.pixel_ind_sps; num_sp=numel(pixel_ind_sps); weight_pool_info=zeros([num_sp, num_units], 'like', one_feat_img); for idx_sp=1:num_sp pixel_ind_sp_one=pixel_ind_sps{idx_sp}; ind_pixels_in_map=pixel_ind_map_org(pixel_ind_sp_one); [ind_units,~,uniqueIndex] = unique(ind_pixels_in_map); frequency = accumarray(uniqueIndex(:),1)./numel(ind_pixels_in_map); frequency=single(frequency); freq_one_sp=zeros(1, num_units, 'single'); freq_one_sp(ind_units)=frequency; weight_pool_info(idx_sp, :)=freq_one_sp; end one_feat_sps=weight_pool_info*one_feat_img; end将上述代码转换为pytorch代码，并可视化超像素的索引】

以下是将给定的 MATLAB 代码转换为 PyTorch 代码的过程：

import torch
import torch.nn.functional as F
import numpy as np
from scipy import ndimage

def do_sp_pooling(one_feat_img, one_sp_info):
    img_size = one_feat_img.shape
    num_units = img_size[0] * img_size[1]
    dim = img_size[2]
    one_feat_img = one_feat_img.reshape(num_units, dim)
    img_size_org = one_sp_info['img_size']
    pixel_ind_map = np.arange(num_units).reshape(img_size[0], img_size[1])
    pixel_ind_map_org = ndimage.zoom(pixel_ind_map, [img_size_org[0]/img_size[0], img_size_org[1]/img_size[1]], order=0)
    pixel_ind_sps = one_sp_info['pixel_ind_sps']
    num_sp = len(pixel_ind_sps)
    weight_pool_info = torch.zeros((num_sp, num_units), dtype=one_feat_img.dtype, device=one_feat_img.device)
    for idx_sp in range(num_sp):
        pixel_ind_sp_one = pixel_ind_sps[idx_sp]
        ind_pixels_in_map = pixel_ind_map_org[pixel_ind_sp_one]
        _, uniqueIndex = np.unique(ind_pixels_in_map, return_inverse=True)
        frequency = np.bincount(uniqueIndex) / len(ind_pixels_in_map)
        frequency = frequency.astype(one_feat_img.dtype)
        freq_one_sp = torch.zeros(num_units, dtype=one_feat_img.dtype, device=one_feat_img.device)
        freq_one_sp[ind_pixels_in_map] = torch.tensor(frequency, dtype=one_feat_img.dtype, device=one_feat_img.device)
        weight_pool_info[idx_sp, :] = freq_one_sp
    one_feat_sps = torch.mm(weight_pool_info, one_feat_img)
    return one_feat_sps, weight_pool_info

这里我们使用了 PyTorch 库中的相关函数来实现对应功能，同时为了可视化超像素的索引，我们可以在函数中增加一些代码：

def do_sp_pooling(one_feat_img, one_sp_info):
    img_size = one_feat_img.shape
    num_units = img_size[0] * img_size[1]
    dim = img_size[2]
    one_feat_img = one_feat_img.reshape(num_units, dim)
    img_size_org = one_sp_info['img_size']
    pixel_ind_map = np.arange(num_units).reshape(img_size[0], img_size[1])
    pixel_ind_map_org = ndimage.zoom(pixel_ind_map, [img_size_org[0]/img_size[0], img_size_org[1]/img_size[1]], order=0)
    pixel_ind_sps = one_sp_info['pixel_ind_sps']
    num_sp = len(pixel_ind_sps)
    weight_pool_info = torch.zeros((num_sp, num_units), dtype=one_feat_img.dtype, device=one_feat_img.device)
    for idx_sp in range(num_sp):
        pixel_ind_sp_one = pixel_ind_sps[idx_sp]
        ind_pixels_in_map = pixel_ind_map_org[pixel_ind_sp_one]
        _, uniqueIndex = np.unique(ind_pixels_in_map, return_inverse=True)
        frequency = np.bincount(uniqueIndex) / len(ind_pixels_in_map)
        frequency = frequency.astype(one_feat_img.dtype)
        freq_one_sp = torch.zeros(num_units, dtype=one_feat_img.dtype, device=one_feat_img.device)
        freq_one_sp[ind_pixels_in_map] = torch.tensor(frequency, dtype=one_feat_img.dtype, device=one_feat_img.device)
        weight_pool_info[idx_sp, :] = freq_one_sp
        # 可视化超像素的索引
        img_sp = np.zeros_like(pixel_ind_map_org)
        img_sp[pixel_ind_sp_one//img_size[1], pixel_ind_sp_one%img_size[1]] = 1
        img_sp = ndimage.binary_dilation(img_sp, iterations=1)
        img_sp = np.where(img_sp, idx_sp+1, 0)
        img_sp = ndimage.zoom(img_sp, [img_size[0]/img_size_org[0], img_size[1]/img_size_org[1]], order=0)
        plt.imshow(img_sp, cmap='jet', alpha=0.3, vmin=0, vmax=num_sp)
    one_feat_sps = torch.mm(weight_pool_info, one_feat_img)
    return one_feat_sps, weight_pool_info

这里我们使用 matplotlib 库来绘制可视化结果，以 jet 颜色映射来表示超像素的索引。

import torch import torch.nn.functional as F import numpy as np from scipy import ndimage def do_sp_pooling(one_feat_img, one_sp_info): img_size = one_feat_img.shape num_units = img_size[0] * img_size[1] dim = img_size[2] one_feat_img = one_feat_img.reshape(num_units, dim) img_size_org = one_sp_info['img_size'] pixel_ind_map = np.arange(num_units).reshape(img_size[0], img_size[1]) pixel_ind_map_org = ndimage.zoom(pixel_ind_map, [img_size_org[0]/img_size[0], img_size_org[1]/img_size[1]], order=0) pixel_ind_sps = one_sp_info['pixel_ind_sps'] num_sp = len(pixel_ind_sps) weight_pool_info = torch.zeros((num_sp, num_units), dtype=one_feat_img.dtype, device=one_feat_img.device) for idx_sp in range(num_sp): pixel_ind_sp_one = pixel_ind_sps[idx_sp] ind_pixels_in_map = pixel_ind_map_org[pixel_ind_sp_one] _, uniqueIndex = np.unique(ind_pixels_in_map, return_inverse=True) frequency = np.bincount(uniqueIndex) / len(ind_pixels_in_map) frequency = frequency.astype(one_feat_img.dtype) freq_one_sp = torch.zeros(num_units, dtype=one_feat_img.dtype, device=one_feat_img.device) freq_one_sp[ind_pixels_in_map] = torch.tensor(frequency, dtype=one_feat_img.dtype, device=one_feat_img.device) weight_pool_info[idx_sp, :] = freq_one_sp one_feat_sps = torch.mm(weight_pool_info, one_feat_img) return one_feat_sps, weight_pool_info，根据上述代码，给出一个详尽的流程

这段代码实现了SP（super-pixel）Pooling的过程，其流程如下：

1.导入必要的库：torch，numpy和scipy中的ndimage。

2.定义一个名为do_sp_pooling的函数，该函数接收两个参数：一个特征图和一个super-pixel信息字典。

3.获取特征图的大小（img_size）和维度（dim），并将特征图重新调整为num_units * dim的形状。

4.获取原始图像的大小（img_size_org）和像素索引映射（pixel_ind_map_org），并使用ndimage.zoom函数将像素索引映射重新调整为原始图像的大小。

5.获取super-pixel信息中的像素索引（pixel_ind_sps）和super-pixel数量（num_sp）。

6.创建一个形状为num_sp * num_units的零张量weight_pool_info，用于存储每个super-pixel对应的像素的权重信息。

7.对于每个super-pixel：

a.获取该super-pixel的像素索引（pixel_ind_sp_one）。

b.使用像素索引映射获取每个像素在像素索引映射中的索引（ind_pixels_in_map）。

c.使用np.unique函数计算ind_pixels_in_map中的唯一值，并返回这些唯一值和它们在ind_pixels_in_map中的索引（uniqueIndex）。

d.使用np.bincount函数计算uniqueIndex中每个唯一值出现的频率，并将其除以ind_pixels_in_map的长度。

e.创建一个零张量freq_one_sp，其形状为num_units，用于存储当前super-pixel的像素在特征图中的权重信息。

f.将频率信息转换为张量，并将其存储到freq_one_sp中，使用ind_pixels_in_map作为索引。

g.将freq_one_sp存储到weight_pool_info的当前super-pixel行中。

8.将weight_pool_info与one_feat_img相乘，得到每个super-pixel的特征表示one_feat_sps。

9.返回one_feat_sps和weight_pool_info。