本文记录了CV算法题的学习。

1 点在多边形内（point in polygon）

参考自文章1，其提供的代码没有考虑一些特殊情况，所以做了改进。
做法：射线法。以待判断点A为端点，画出方向水平朝右的射线，统计该射线与多边形B的交点个数。奇数：内，偶数：外。(需考虑点A是否在B的某个点或边上是否有平行的边。)
图片来自：https://www.jianshu.com/p/ba03c600a557。

代码：

def is_in_poly(p, poly):""":param p: [x, y]:param poly: [[], [], [], [], ...]:return:"""px, py = pis_in = Falsefor i, corner in enumerate(poly):next_i = i + 1 if i + 1 < len(poly) else 0x1, y1 = cornerx2, y2 = poly[next_i]if (x1 == px and y1 == py) or (x2 == px and y2 == py):  # 点p是否在多边形的某个点上is_in = Truebreakif y1 == y2 :  #边是水平的，如果点在边上则break，如果不在，则跳过这一轮判断if  min(x1, x2) < px < max(x1, x2)and y1==py: is_in = Truebreakelif min(y1, y2) <= py <= max(y1, y2):  #边不是水平的x = x1 + (py - y1) * (x2 - x1) / (y2 - y1)if x == px:  # 点是否在射线上is_in = Truebreakelif x > px:  # 点是否在边左侧，即射线是否穿过边is_in = not is_inreturn is_inif __name__ == '__main__':#第一组，内point = [3, 10/7] poly = [[0, 0], [7, 3], [8, 8], [5, 5]]print(is_in_poly(point, poly))#第二组，外point = [3, 8/7]poly = [[0, 0], [7, 3], [8, 8], [5, 5]]print(is_in_poly(point, poly))#第三组，有平行边，射线与边重合，外point = [-2, 0]poly = [[0, 0], [7, 0], [7, 8], [5, 5]]print(is_in_poly(point, poly))#第四组，有平行边，射线与边重合，内point = [2, 0]poly = [[0, 0], [7, 0], [7, 8], [5, 5]]print(is_in_poly(point, poly))#第五组，在某点上point = [7, 3] poly = [[0, 0], [7, 3], [8, 8], [5, 5]]print(is_in_poly(point, poly))

2 高斯滤波器

参考文章2
高斯滤波器为线性平滑滤波器，通常假定图像包含高斯白噪声，可以通过高斯滤波来抑制噪声。
二维高斯分布公式：

其中的ux和uy是中心点坐标。

3x3滤波核的生成：

1. 先得到相对于中心点的坐标模板。
   
2. 根据公式和坐标模板得到滤波核的每个位置的值。当标准差$\sigma$为1.3时，得到的整数形式的滤波核为：
   

代码：

import cv2import numpy as np# Gaussian filterdef gaussian_filter(img, K_size=3, sigma=1.3):if len(img.shape) == 3:H, W, C = img.shapeelse:img = np.expand_dims(img, axis=-1)H, W, C = img.shape## Zero paddingpad = K_size // 2out = np.zeros((H + pad * 2, W + pad * 2, C), dtype=np.float)out[pad: pad + H, pad: pad + W] = img.copy().astype(np.float)## prepare KernelK = np.zeros((K_size, K_size), dtype=np.float)for x in range(-pad, -pad + K_size):for y in range(-pad, -pad + K_size):K[y + pad, x + pad] = np.exp( -(x ** 2 + y ** 2) / (2 * (sigma ** 2)))K /= (2 * np.pi * sigma * sigma)K /= K.sum() #归一化print(K)K=K[:,:,np.newaxis].repeat(C,axis=2)# 扩展维度至（K_size,K_size,C）print(K[:,:,0])print(K[:,:,1])tmp = out.copy()# filteringfor y in range(H):for x in range(W):# for c in range(C):out[pad + y, pad + x, :] = np.sum(np.sum(K * tmp[y: y + K_size, x: x + K_size, :],axis=0),axis=0)out = np.clip(out, 0, 255)out = out[pad: pad + H, pad: pad + W].astype(np.uint8)return out# Read image
img = cv2.imread("./lena.png")# Gaussian Filter
out = gaussian_filter(img, K_size=3, sigma=1.3)# Save result
cv2.imwrite("out.jpg", out)
cv2.imshow("result", out)
cv2.imshow("origin", img) 
cv2.waitKey(0)
cv2.destroyAllWindows()

结果：

3 ViT

论文，参考文章3，代码来源。

Patch Embedding

作用：将图像切块，得到用向量表示的图像局部信息。减少了计算和存储开销。
ViT中，利用卷积实现，卷积核kernel与步长stride取相同的值patchsize。
设原图像大小为224x224，patchsize为16，则经过patchembedding后，得到的patch数量为：
$(224/16)\ast (224/16)=196$
代码：

import torch
import torch.nn as nn
import cv2
import torchvision.transforms as transforms
class PatchEmbed(nn.Module):"""2D Image to Patch Embedding"""def __init__(self, img_size=224, patch_size=16, in_c=3, embed_dim=768, norm_layer=None):super().__init__()img_size = (img_size, img_size)patch_size = (patch_size, patch_size)self.img_size = img_sizeself.patch_size = patch_sizeself.grid_size = (img_size[0] // patch_size[0], img_size[1] // patch_size[1])self.num_patches = self.grid_size[0] * self.grid_size[1] #patchembedding后，patch数量self.proj = nn.Conv2d(in_c, embed_dim, kernel_size=patch_size, stride=patch_size)self.norm = norm_layer(embed_dim) if norm_layer else nn.Identity()def forward(self, x):B, C, H, W = x.shapeassert H == self.img_size[0] and W == self.img_size[1], \f"Input image size ({H}*{W}) doesn't match model ({self.img_size[0]}*{self.img_size[1]})."# flatten: [B, C, H, W] -> [B, C, HW]# transpose: [B, C, HW] -> [B, HW, C]x = self.proj(x).flatten(2).transpose(1, 2)x = self.norm(x)return xif __name__ == '__main__':img = cv2.resize(cv2.imread("./lena.png"),(224,224))trans = transforms.ToTensor()imgtensor = trans(img).unsqueeze(0)print(imgtensor.shape)patch  = PatchEmbed(img_size=imgtensor.shape[2])print(patch.num_patches)print(patch(imgtensor).shape)

结果：

Position Embedding

patch处理后，每个块之间是没有顺序信息的，所以需要添加位置信息。
在VisionTransformer中定义self.pos_embed = nn.Parameter(torch.zeros(1, num_patches + self.num_tokens, embed_dim))
其中的self.num_tokens是1或2，对应一个cls token和一个distilled token(后者没用，他是DeiT的结构)

Transformer Encoder

Transformer Encoder将序列[196+1,768]进行编码，其结果如ViT框架图的右侧。

Multi-head Attention 代码：先通过linear映射得到q k v，然后进行矩阵乘法(除以scale避免值溢出)得到attention，然后矩阵乘法得到输出结果(concat所有head，然后再通过一个linear层)。

class Attention(nn.Module):def __init__(self,dim,   # 输入token的dimnum_heads=8,qkv_bias=False,qk_scale=None,attn_drop_ratio=0.,proj_drop_ratio=0.):super(Attention, self).__init__()self.num_heads = num_headshead_dim = dim // num_heads #多头，计算每个头的dimself.scale = qk_scale or head_dim ** -0.5 # 这对应attention里的根号下dk，避免qk内积值过大导致溢出。self.qkv = nn.Linear(dim, dim * 3, bias=qkv_bias) self.attn_drop = nn.Dropout(attn_drop_ratio)self.proj = nn.Linear(dim, dim)self.proj_drop = nn.Dropout(proj_drop_ratio)def forward(self, x):# [batch_size, num_patches + 1, total_embed_dim]B, N, C = x.shape# qkv(): -> [batch_size, num_patches + 1, 3 * total_embed_dim]# reshape: -> [batch_size, num_patches + 1, 3, num_heads, embed_dim_per_head]# permute: -> [3, batch_size, num_heads, num_patches + 1, embed_dim_per_head]qkv = self.qkv(x).reshape(B, N, 3, self.num_heads, C // self.num_heads).permute(2, 0, 3, 1, 4)# [batch_size, num_heads, num_patches + 1, embed_dim_per_head]q, k, v = qkv[0], qkv[1], qkv[2]  # make torchscript happy (cannot use tensor as tuple)# transpose: -> [batch_size, num_heads, embed_dim_per_head, num_patches + 1]# @: multiply -> [batch_size, num_heads, num_patches + 1, num_patches + 1]attn = (q @ k.transpose(-2, -1)) * self.scale # 除以根号下dk等于乘以dk的负0.5次方attn = attn.softmax(dim=-1) attn = self.attn_drop(attn)# @: multiply -> [batch_size, num_heads, num_patches + 1, embed_dim_per_head]# transpose: -> [batch_size, num_patches + 1, num_heads, embed_dim_per_head]# reshape: -> [batch_size, num_patches + 1, total_embed_dim]x = (attn @ v).transpose(1, 2).reshape(B, N, C)x = self.proj(x)x = self.proj_drop(x)return x

MLP 代码：2层linear实现，都有drop防止过拟合，第一层还有激活函数。

class Mlp(nn.Module):def __init__(self, in_features, hidden_features=None, out_features=None, act_layer=nn.GELU, drop=0.):super().__init__()out_features = out_features or in_featureshidden_features = hidden_features or in_featuresself.fc1 = nn.Linear(in_features, hidden_features) self.act = act_layer() #激活函数self.fc2 = nn.Linear(hidden_features, out_features)self.drop = nn.Dropout(drop) #2层linear共用，def forward(self, x):x = self.fc1(x)x = self.act(x)x = self.drop(x)x = self.fc2(x)x = self.drop(x)return x

Encoder Block 代码：通过上面的Attention和MLP实现block。输入x先通过norm1归一化，再attention，然后通过norm2和mlp。代码中有一个drop_path，它和droupout一样是用于防止过拟合的。后者是随机将batch中的某些值置0，前者是将batch中某个样本的所有值置0。

class Block(nn.Module):def __init__(self,dim,num_heads,mlp_ratio=4.,qkv_bias=False,qk_scale=None,drop_ratio=0.,attn_drop_ratio=0.,drop_path_ratio=0.,act_layer=nn.GELU,norm_layer=nn.LayerNorm):super(Block, self).__init__()self.norm1 = norm_layer(dim)self.attn = Attention(dim, num_heads=num_heads, qkv_bias=qkv_bias, qk_scale=qk_scale,attn_drop_ratio=attn_drop_ratio, proj_drop_ratio=drop_ratio)# NOTE: drop path for stochastic depth, we shall see if this is better than dropout hereself.drop_path = DropPath(drop_path_ratio) if drop_path_ratio > 0. else nn.Identity()self.norm2 = norm_layer(dim)mlp_hidden_dim = int(dim * mlp_ratio)self.mlp = Mlp(in_features=dim, hidden_features=mlp_hidden_dim, act_layer=act_layer, drop=drop_ratio)def forward(self, x):x = x + self.drop_path(self.attn(self.norm1(x)))x = x + self.drop_path(self.mlp(self.norm2(x)))return x

完整的ViT模型

class VisionTransformer(nn.Module):def __init__(self, img_size=224, patch_size=16, in_c=3, num_classes=1000,embed_dim=768, depth=12, num_heads=12, mlp_ratio=4.0, qkv_bias=True,qk_scale=None, representation_size=None, distilled=False, drop_ratio=0.,attn_drop_ratio=0., drop_path_ratio=0., embed_layer=PatchEmbed, norm_layer=None,act_layer=None):super(VisionTransformer, self).__init__()self.num_classes = num_classesself.num_features = self.embed_dim = embed_dim  # num_features for consistency with other modelsself.num_tokens = 2 if distilled else 1norm_layer = norm_layer or partial(nn.LayerNorm, eps=1e-6)act_layer = act_layer or nn.GELUself.patch_embed = embed_layer(img_size=img_size, patch_size=patch_size, in_c=in_c, embed_dim=embed_dim)num_patches = self.patch_embed.num_patchesself.cls_token = nn.Parameter(torch.zeros(1, 1, embed_dim))self.dist_token = nn.Parameter(torch.zeros(1, 1, embed_dim)) if distilled else Noneself.pos_embed = nn.Parameter(torch.zeros(1, num_patches + self.num_tokens, embed_dim))self.pos_drop = nn.Dropout(p=drop_ratio)dpr = [x.item() for x in torch.linspace(0, drop_path_ratio, depth)]  # stochastic depth decay ruleself.blocks = nn.Sequential(*[Block(dim=embed_dim, num_heads=num_heads, mlp_ratio=mlp_ratio, qkv_bias=qkv_bias, qk_scale=qk_scale,drop_ratio=drop_ratio, attn_drop_ratio=attn_drop_ratio, drop_path_ratio=dpr[i],norm_layer=norm_layer, act_layer=act_layer)for i in range(depth)])self.norm = norm_layer(embed_dim)# Representation layerif representation_size and not distilled:self.has_logits = Trueself.num_features = representation_sizeself.pre_logits = nn.Sequential(OrderedDict([("fc", nn.Linear(embed_dim, representation_size)),("act", nn.Tanh())]))else:self.has_logits = Falseself.pre_logits = nn.Identity()# Classifier head(s)self.head = nn.Linear(self.num_features, num_classes) if num_classes > 0 else nn.Identity()self.head_dist = Noneif distilled:self.head_dist = nn.Linear(self.embed_dim, self.num_classes) if num_classes > 0 else nn.Identity()# Weight initnn.init.trunc_normal_(self.pos_embed, std=0.02)if self.dist_token is not None:nn.init.trunc_normal_(self.dist_token, std=0.02)nn.init.trunc_normal_(self.cls_token, std=0.02)self.apply(_init_vit_weights)def forward_features(self, x):# [B, C, H, W] -> [B, num_patches, embed_dim]x = self.patch_embed(x)  # [B, 196, 768]# [1, 1, 768] -> [B, 1, 768]cls_token = self.cls_token.expand(x.shape[0], -1, -1)if self.dist_token is None:x = torch.cat((cls_token, x), dim=1)  # [B, 197, 768]else:x = torch.cat((cls_token, self.dist_token.expand(x.shape[0], -1, -1), x), dim=1)x = self.pos_drop(x + self.pos_embed)x = self.blocks(x)x = self.norm(x)if self.dist_token is None:return self.pre_logits(x[:, 0])else:return x[:, 0], x[:, 1]def forward(self, x):x = self.forward_features(x) #1 patch、2cat cls_token、3加位置编码并dropout、4通过depth个encoder block、5norm归一化、6将cls_token通过self.pre_logits(1层linear和1层tanh激活层)if self.head_dist is not None: #不执行x, x_dist = self.head(x[0]), self.head_dist(x[1])if self.training and not torch.jit.is_scripting():# during inference, return the average of both classifier predictionsreturn x, x_distelse:return (x + x_dist) / 2else: #执行,通过分类头x = self.head(x)return x

4 SE模块

论文。

作用：自适应学习通道间的关系。
模块流程：输入X经过卷积卷积Fr(·)得到特征图U，U经过SE模块得到信息矫正后的特征图。
组成：

1. Squeeze操作通过全局平均池化将特征图的空间维度压缩为1(称为通道描述符)，获取全局信息。
2. Excitation操作通过2层linear(有激活函数)对通道描述符进行加权，学习到更具价值的权重值。

代码：

import torch
import torch.nn as nn
class SE(nn.Module):def __init__(self, in_chnls, ratio):super(SE, self).__init__()self.squeeze = nn.AdaptiveAvgPool2d((1, 1))self.excitation =nn.Sequential(nn.Linear(in_chnls, in_chnls//ratio,bias=False),nn.ReLU(inplace=True),nn.Linear(in_chnls//ratio, in_chnls,bias=False),nn.Sigmoid()    )def forward(self, x):out = self.squeeze(x)out = out.squeeze()out = self.excitation(out).unsqueeze(-1).unsqueeze(-1)print("out_shape: ",out.shape)return x+out.expand_as(x)if __name__ == "__main__":U = torch.randn((2,256,32,32))print("U_shape: ",U.shape)se = SE(256,4)U_se = se(U)

5 Dense Block

论文，参考文章5_1和文章5_2。

dense block：每一层的输出与之前的所有层的输出concat，作为下一层的输入。
优势：

1. 实现了比resnet(与前一层进行像素级相加)更密集的连接方式。
2. 每层都与最后的loss有更直接的连接，使得特征利用更充分，减少了冗余的参数量。
3. 缓解梯度消失，加速收敛。

代码：

import torch
import torch.functional as Ffrom torch import nnclass BN_Conv2d(nn.Module):"""CONV_BN_RELU"""def __init__(self, in_channels: object, out_channels: object, kernel_size: object, stride: object, padding: object,dilation=1, groups=1, bias=False) -> object:super(BN_Conv2d, self).__init__()self.seq = nn.Sequential(nn.Conv2d(in_channels, out_channels, kernel_size=kernel_size, stride=stride,padding=padding, dilation=dilation, groups=groups, bias=bias),nn.BatchNorm2d(out_channels),nn.ReLU(inplace=True))def forward(self, x):return self.seq(x)class DenseBlock(nn.Module):def __init__(self, input_channels, num_layers, growth_rate):super(DenseBlock, self).__init__()self.num_layers = num_layers self.k0 = input_channels #输入通道数self.k = growth_rate #每一个layer的输出通道数self.layers = self.__make_layers()def __make_layers(self):layer_list = []for i in range(self.num_layers):layer_list.append(nn.Sequential(BN_Conv2d(self.k0+i*self.k, 4*self.k, 1, 1, 0),BN_Conv2d(4 * self.k, self.k, 3, 1, 1)))return layer_listdef forward(self, x):feature = self.layers[0](x) #B,self.k,H,Wout = torch.cat((x, feature), 1) #B,self.k0+self.k,H,Wfor i in range(1, len(self.layers)):feature = self.layers[i](out) #B,self.k,H,Wout = torch.cat((feature, out), 1) #B,self.k0+(i+1)*self.k,H,Wreturn out
if __name__ == "__main__":denseblock =DenseBlock(256,2,32)print("denseblock.layers: "denseblock.layers)x = torch.randn((2,256,32,32))out = denseblock(x)print("out_shape: ",out.shape)

结果：

6 Batch Normalization