1、功能描述

利用液化效果实现瘦脸美颜

交互式的液化效果原理来自 Gustafsson A. Interactive image warping[D]. , 1993.

2、原理分析

上面描述很清晰了，鼠标初始在 C，也即形变范围的圆心在 C，形变半径 $r_{max}$，形变方向 C→M，

圆圈内原始 U 位置会被形变到 X，可以简单直白理解为拉伸后 U 位置的值给了 X 位置，此时 U 位置空置了，需要插值

插值公示 93 年的论文中直接给出了，我们尝试 coding

这里还涉及到插值，我们回顾下比较常见的双线性插值原理

3、代码实现

导入必要的库函数

import dlib
import cv2
import numpy as np
import math

载入人脸检测器和人脸关键点检测模型

predictor_path = "./shape_predictor_68_face_landmarks.dat"# 使用dlib自带的frontal_face_detector作为我们的特征提取器
detector = dlib.get_frontal_face_detector()  # 人脸检测器
predictor = dlib.shape_predictor(predictor_path)  # 关键点检测模型

读入图片，调用 face_thin_auto 函数，实现瘦脸

def main():src = cv2.imread(r'./1.jpg')  # (1546, 1236, 3)# cv2.imshow('src', src)face_thin_auto(src)cv2.waitKey(0)if __name__ == '__main__':main()

看看 face_thin_auto 函数的实现细节

def face_thin_auto(src):landmarks = landmark_dec_dlib_fun(src)point_img = src.copy()for index, landmark in enumerate(landmarks[0]):cv2.circle(point_img, center=np.array(landmark)[0], radius=5, color=(255, 0, 0), thickness=-1)cv2.putText(point_img, str(index), org=(landmark[0,0]-30, landmark[0,1]),fontFace=cv2.FONT_HERSHEY_TRIPLEX,fontScale=0.5, color=(0,255,0))cv2.imwrite("point.jpg", point_img)# 如果未检测到人脸关键点，就不进行瘦脸if len(landmarks) == 0:print("not detect face keypoint")returnthin_image = srclandmarks_node = landmarks[0]endPt = landmarks_node[16]  # matrix([[753, 450]])for index in range(3, 14, 2):start_landmark = landmarks_node[index]end_landmark = landmarks_node[index + 2]r = math.sqrt((start_landmark[0, 0] - end_landmark[0, 0]) **2 +(start_landmark[0, 1] - end_landmark[0, 1]) **2)thin_image = localTranslationWarp(thin_image, start_landmark[0, 0],start_landmark[0, 1], endPt[0, 0], endPt[0, 1], r)# 显示# cv2.imshow('thin', thin_image)cv2.imwrite(r'./thin.jpg', thin_image)

landmark_dec_dlib_fun 检测人脸和人脸关键点，实现如下

def landmark_dec_dlib_fun(img_src):img_gray = cv2.cvtColor(img_src, cv2.COLOR_BGR2GRAY)cv2.imwrite("gray.jpg", img_gray)land_marks = []rects = detector(img_gray, 0)  # 人脸检测，[[(336, 286) (782, 732)]]plot_img = img_src.copy()for i in range(len(rects)):  # 遍历检测到的人脸cv2.rectangle(plot_img, (rects[i].left(), rects[i].top()),  (rects[i].right(), rects[i].bottom()),color=(0,255,0), thickness=10)land_marks_node = np.matrix([[p.x, p.y] for p in predictor(img_gray, rects[i]).parts()])land_marks.append(land_marks_node)cv2.imwrite("face_det.jpg", plot_img)return land_marks

先把图片变成灰度图，然后人脸检测，绘制人脸检测结果，人脸关键点检测，返回关键点坐标

face_thin_auto 函数接下来绘制人脸关键点，一共 68 个

遍历关键点，3，5，7，9，11，13

也即 C = 3，5，7，9，11，13，M = 16

$r_{max}$ 为关键点 3-5 的距离，5-7 的距离，7-9 的距离，9-11 的距离，11-13 的距离，13-15 的距离

调用 localTranslationWarp 求瘦脸后的图片，

def localTranslationWarp(srcImg, startX, startY, endX, endY, radius):ddradius = float(radius * radius)copyImg = srcImg.copy()# 计算公式中的|m-c|^2ddmc = (endX - startX) ** 2 + (endY - startY) ** 2H, W, C = srcImg.shapefor i in range(W):for j in range(H):# 计算该点是否在形变圆的范围之内# 优化，第一步，直接判断是会在（startX,startY)的矩阵框中if math.fabs(i - startX) > radius and math.fabs(j - startY) > radius:continue  # 不在 continuedistance = (i - startX) ** 2 + (j - startY) ** 2if (distance < ddradius):# 计算出（i,j）坐标的原坐标# 计算公式中右边平方号里的部分ratio = (ddradius - distance) / (ddradius - distance + ddmc)ratio = ratio ** 2# 映射原位置UX = i - ratio * (endX - startX)UY = j - ratio * (endY - startY)# 根据双线性插值法得到UX，UY的值value = BilinearInsert(srcImg, UX, UY)# 改变当前 i ，j的值copyImg[j, i] = valuereturn copyImg

localTranslationWarp 仅作用与以 C 为圆心，$r_{max}$ 范围内的像素点，像素点的坐标求法代入公式计算，值用插值求出

双线性插值实现

def BilinearInsert(src, ux, uy):w, h, c = src.shapeif c == 3:x1 = int(ux)x2 = x1 + 1y1 = int(uy)y2 = y1 + 1part1 = src[y1, x1].astype(float) * (float(x2) - ux) * (float(y2) - uy)part2 = src[y1, x2].astype(float) * (ux - float(x1)) * (float(y2) - uy)part3 = src[y2, x1].astype(float) * (float(x2) - ux) * (uy - float(y1))part4 = src[y2, x2].astype(float) * (ux - float(x1)) * (uy - float(y1))insertValue = part1 + part2 + part3 + part4return insertValue.astype(np.int8)

我们看看

        part1 = src[y1, x1].astype(float) * (float(x2) - ux) * (float(y2) - uy)part2 = src[y1, x2].astype(float) * (ux - float(x1)) * (float(y2) - uy)part3 = src[y2, x1].astype(float) * (float(x2) - ux) * (uy - float(y1))part4 = src[y2, x2].astype(float) * (ux - float(x1)) * (uy - float(y1))

对应

$f(Q_{11})\ast \frac{x_2-x}{x_2-x_1}\ast \frac{y_2-y}{y_2-y_1}=f(Q_{11})\ast (x_2-x)\ast (y_2-y)$

$f(Q_{21})\ast \frac{x-x_1}{x_2-x_1}\ast \frac{y_2-y}{y_2-y_1}=f(Q_{21})\ast (x-x_1)\ast (y_2-y)$

$f(Q_{12})\ast \frac{x_2-x}{x_2-x_1}\ast \frac{y-y_1}{y_2-y_1}=f(Q_{12})\ast (x_2-x)\ast (y-y_1)$

$f(Q_{22})\ast \frac{x-x_1}{x_2-x_1}\ast \frac{y-y_1}{y_2-y_1}=f(Q_{22})\ast (x-x_1)\ast (y-y_1)$

4、效果展示

输入

输出

再明显一点试试

输入

输出

肉眼看不太明显，对比工具看比较明显

缩小下图片的输入分辨率

效果会明显一些

5、完整代码

import dlib
import cv2
import numpy as np
import mathpredictor_path = "./shape_predictor_68_face_landmarks.dat"# 使用dlib自带的frontal_face_detector作为我们的特征提取器
detector = dlib.get_frontal_face_detector()
predictor = dlib.shape_predictor(predictor_path)def landmark_dec_dlib_fun(img_src):img_gray = cv2.cvtColor(img_src, cv2.COLOR_BGR2GRAY)cv2.imwrite("gray.jpg", img_gray)land_marks = []rects = detector(img_gray, 0)  # 人脸检测，[[(336, 286) (782, 732)]]plot_img = img_src.copy()for i in range(len(rects)):  # 遍历检测到的人脸cv2.rectangle(plot_img, (rects[i].left(), rects[i].top()),  (rects[i].right(), rects[i].bottom()),color=(0,255,0), thickness=10)land_marks_node = np.matrix([[p.x, p.y] for p in predictor(img_gray, rects[i]).parts()])land_marks.append(land_marks_node)cv2.imwrite("face_det.jpg", plot_img)return land_marks'''
方法： Interactive Image Warping 局部平移算法
'''
def localTranslationWarp(srcImg, startX, startY, endX, endY, radius):ddradius = float(radius * radius)copyImg = srcImg.copy()# 计算公式中的|m-c|^2ddmc = (endX - startX) ** 2 + (endY - startY) ** 2H, W, C = srcImg.shapefor i in range(W):for j in range(H):# 计算该点是否在形变圆的范围之内# 优化，第一步，直接判断是会在（startX,startY)的矩阵框中if math.fabs(i - startX) > radius and math.fabs(j - startY) > radius:continue  # 不在 continuedistance = (i - startX) ** 2 + (j - startY) ** 2if (distance < ddradius):# 计算出（i,j）坐标的原坐标# 计算公式中右边平方号里的部分ratio = (ddradius - distance) / (ddradius - distance + ddmc)ratio = ratio ** 2# 映射原位置UX = i - ratio * (endX - startX)UY = j - ratio * (endY - startY)# 根据双线性插值法得到UX，UY的值value = BilinearInsert(srcImg, UX, UY)# 改变当前 i ，j的值copyImg[j, i] = valuereturn copyImg# 双线性插值法
def BilinearInsert(src, ux, uy):w, h, c = src.shapeif c == 3:x1 = int(ux)x2 = x1 + 1y1 = int(uy)y2 = y1 + 1part1 = src[y1, x1].astype(float) * (float(x2) - ux) * (float(y2) - uy)part2 = src[y1, x2].astype(float) * (ux - float(x1)) * (float(y2) - uy)part3 = src[y2, x1].astype(float) * (float(x2) - ux) * (uy - float(y1))part4 = src[y2, x2].astype(float) * (ux - float(x1)) * (uy - float(y1))insertValue = part1 + part2 + part3 + part4return insertValue.astype(np.int8)def face_thin_auto(src):landmarks = landmark_dec_dlib_fun(src)point_img = src.copy()for index, landmark in enumerate(landmarks[0]):cv2.circle(point_img, center=np.array(landmark)[0], radius=5, color=(255, 0, 0), thickness=-1)cv2.putText(point_img, str(index), org=(landmark[0,0]-30, landmark[0,1]),fontFace=cv2.FONT_HERSHEY_TRIPLEX,fontScale=0.5, color=(0,255,0))cv2.imwrite("point.jpg", point_img)# 如果未检测到人脸关键点，就不进行瘦脸if len(landmarks) == 0:print("not detect face keypoint")returnthin_image = srclandmarks_node = landmarks[0]endPt = landmarks_node[16]  # matrix([[753, 450]])for index in range(3, 14, 2):start_landmark = landmarks_node[index]end_landmark = landmarks_node[index + 2]r = math.sqrt((start_landmark[0, 0] - end_landmark[0, 0]) **2 +(start_landmark[0, 1] - end_landmark[0, 1]) **2)thin_image = localTranslationWarp(thin_image, start_landmark[0, 0],start_landmark[0, 1], endPt[0, 0], endPt[0, 1], r)# 显示# cv2.imshow('thin', thin_image)cv2.imwrite(r'./thin.jpg', thin_image)def main():src = cv2.imread(r'./1.jpg')  # (1546, 1236, 3)# cv2.imshow('src', src)face_thin_auto(src)cv2.waitKey(0)if __name__ == '__main__':main()

6、参考

• http://dlib.net/files/
  shape_predictor_68_face_landmarks.dat.bz2

• 链接: https://pan.baidu.com/s/1gO_wqRAtWndGkUhZOSBw2Q?pwd=4enn
  提取码: 4enn

• 图像变形算法:实现Photoshop液化工具箱中向前变形工具

• http://www.gson.org/thesis/warping-thesis.pdf

• 图像处理算法之瘦脸及放大眼睛

• 图像瘦脸算法

• 简易版“美颜”来了！肝了一夜！用Python做一个高瘦脸神器！

• OpenCV图像处理|Python OpenCV实现人脸瘦脸功能

• pytorch 液态算法实现瘦脸效果

• 双线性插值算法原理 python实现

• 双线性插值法

• 双线性插值

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