CV算法面试题学习

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 = p
    is_in = False
    for i, corner in enumerate(poly):
        next_i = i + 1 if i + 1 < len(poly) else 0
        x1, y1 = corner
        x2, 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 = True
            break
        if 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 = True
                break
        elif 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 = True
                break
            elif x > px:  # 点是否在边左侧，即射线是否穿过边
                is_in = not is_in

    return is_in
 
 
if __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 cv2
 
import numpy as np
 
# Gaussian filter
 
def gaussian_filter(img, K_size=3, sigma=1.3):
 
    if len(img.shape) == 3:
        H, W, C = img.shape
    else:
        img = np.expand_dims(img, axis=-1)
        H, W, C = img.shape
 
    ## Zero padding
    pad = K_size // 2
    out = 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 Kernel
    K = 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()
 
    # filtering
    for 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_size
        self.patch_size = patch_size
        self.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.shape
        assert 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 x

if __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dim
                 num_heads=8,
                 qkv_bias=False,
                 qk_scale=None,
                 attn_drop_ratio=0.,
                 proj_drop_ratio=0.):
        super(Attention, self).__init__()
        self.num_heads = num_heads
        head_dim = dim // num_heads #多头，计算每个头的dim
        self.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_features
        hidden_features = hidden_features or in_features
        self.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 here
        self.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_classes
        self.num_features = self.embed_dim = embed_dim  # num_features for consistency with other models
        self.num_tokens = 2 if distilled else 1
        norm_layer = norm_layer or partial(nn.LayerNorm, eps=1e-6)
        act_layer = act_layer or nn.GELU

        self.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_patches

        self.cls_token = nn.Parameter(torch.zeros(1, 1, embed_dim))
        self.dist_token = nn.Parameter(torch.zeros(1, 1, embed_dim)) if distilled else None
        self.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 rule
        self.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 layer
        if representation_size and not distilled:
            self.has_logits = True
            self.num_features = representation_size
            self.pre_logits = nn.Sequential(OrderedDict([
                ("fc", nn.Linear(embed_dim, representation_size)),
                ("act", nn.Tanh())
            ]))
        else:
            self.has_logits = False
            self.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 = None
        if distilled:
            self.head_dist = nn.Linear(self.embed_dim, self.num_classes) if num_classes > 0 else nn.Identity()

        # Weight init
        nn.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 predictions
                return x, x_dist
            else:
                return (x + x_dist) / 2
        else: #执行,通过分类头
            x = self.head(x)
        return x

4 SE模块