从0到1，反距离加权IDW(Inverse Distance Weighted Interpolation) 插值变形算法_idwinterpolation

论文：

Image Warping with Scattered Image Warping with Scattered Data Interpolation

局部变形算法：液化，膨胀

全局变形算法：IDW，MLS，特征线变形

算法思路：

算法优缺点：

优点：实现简单，cpu实现，gpu实现都友好

缺点：速度与点的个数，图片长，宽，这3个指标成正比，点个数越多，速度越慢，图片越大速度越慢。如果点太少，形变会不平滑。

应用场景：

大脸，瘦脸，大眼，等任何形变场景

基本实现：

好处，更容易结合公式看清原理，缺点，速度很慢。

class IDW(object):
    def __init__(self,):
        pass
 
    def IDW(self, srcImg, input_points, output_points):
        start = time.time()
        height, width, _ = srcImg.shape
        keypoints_num = len(input_points)
        
        u = 2
        UX =  np.expand_dims(np.vstack([np.arange(width).astype(np.float32).reshape(1, -1)] * height), axis = 2)
        UY =  np.expand_dims(np.hstack([np.arange(height).astype(np.float32).reshape(-1, 1)] * width), axis = 2)
 
        input_points_X = np.ones((height,width,keypoints_num), np.float32) * input_points[:,0]
        input_points_Y = np.ones((height,width,keypoints_num), np.float32) * input_points[:,1]
        output_points_X = np.ones((height,width,keypoints_num), np.float32) * output_points[:,0]
        output_points_Y = np.ones((height,width,keypoints_num), np.float32) * output_points[:,1]
 
 
        v_tmp = np.power( (UX - input_points_X)*(UX - input_points_X) + (UY - input_points_Y)*(UY - input_points_Y), u)
        for k in range(keypoints_num):
            v_tmp[input_points[k,1],input_points[k,0],:] = 1
 
        v = 1/v_tmp
        ww = np.expand_dims(1/np.sum(v,axis = 2), axis =2)
        UX = np.squeeze( (np.sum(v*(output_points_X + UX - input_points_X), axis = 2, keepdims=True)) * ww).astype(np.float32)
        UY = np.squeeze( (np.sum(v*(output_points_Y + UY - input_points_Y), axis = 2, keepdims=True)) * ww).astype(np.float32)
 
        copyImg = cv2.remap(srcImg, UX, UY, interpolation=cv2.INTER_LINEAR)
        end = time.time()
        print("IDW time cost:{} s".format(end - start))
        return copyImg

numba向量化加速实现：

好处，基于向量化实现，速度更快，缺点，没有足够快 

from numba import jit, vectorize, int64, float64, njit, prange
    def IDW(self, srcImg, input_points, output_points):
        @vectorize([float64(float64,float64, float64, float64, int64)], target='parallel')
        def l2_power_numba(UX, input_points_X, UY, input_points_Y, u):
            tmp_x = UX - input_points_X
            tmp_y = UY - input_points_Y
            ux_sum = tmp_x * tmp_x
            uy_sum = tmp_y * tmp_y
            if u==1:
                return ux_sum + uy_sum
            else:
                return np.power(ux_sum + uy_sum, u)
 
 
        @vectorize([float64(float64)], target='parallel')
        def div_numba(v_tmp):
            return 1/v_tmp
 
 
        start = time.time()
        height, width, _ = srcImg.shape
        keypoints_num = len(input_points)
        
        u = 2
 
        UX =  np.expand_dims(np.vstack([np.arange(width).astype(np.float32).reshape(1, -1)] * height), axis = 2)
        UY =  np.expand_dims(np.hstack([np.arange(height).astype(np.float32).reshape(-1, 1)] * width), axis = 2)
 
        input_points_X = np.ones((1,1,keypoints_num), np.float32)
        input_points_X = input_points[:,0]
        input_points_Y = np.ones((1,1,keypoints_num), np.float32)
        input_points_Y = input_points[:,1]
        output_points_X = np.ones((1,1,keypoints_num), np.float32)
        output_points_X = output_points[:,0]
        output_points_Y = np.ones((1,1,keypoints_num), np.float32)
        output_points_Y = output_points[:,1]
 
 
        v_tmp = l2_power_numba(UX, input_points_X, UY, input_points_Y, u)
 
 
        for k in range(keypoints_num):
            v_tmp[input_points[k,1],input_points[k,0],:] = v_tmp[input_points[k,1]-1,input_points[k,0]-1,:]
 
 
        v = div_numba(v_tmp)
        ww = np.expand_dims(1/np.sum(v,axis = 2), axis =2)
 
    
        UX = np.squeeze( UX + np.sum(v * (output_points_X- input_points_X), axis=2, keepdims=True) * ww).astype(np.float32)
        UY = np.squeeze( UY + np.sum(v * (output_points_Y- input_points_Y), axis=2, keepdims=True) * ww).astype(np.float32)
 
 
        copyImg = cv2.remap(srcImg, UX, UY, interpolation=cv2.INTER_LINEAR)
        end = time.time()
        print("IDW FAST time cost:{} s".format(end - start))
 
        return copyImg

cpu最佳加速实现：

好处，基于scipy加速计算距离，公式合并，减少一次乘法，2d矩阵变1d矩阵。

from scipy.spatial.distance import cdist
class IDW(object):
    def __init__(self,
                 original_control_points=None,
                 deformed_control_points=None,
                 power=1):
 
        if original_control_points is None:
            self.original_control_points = np.array([[0., 0., 0.], [0., 0., 1.],
                                                     [0., 1., 0.], [1., 0., 0.],
                                                     [0., 1., 1.], [1., 0., 1.],
                                                     [1., 1., 0.], [1., 1.,
                                                                    1.]])
        else:
            self.original_control_points = original_control_points
 
        if deformed_control_points is None:
            self.deformed_control_points = np.array([[0., 0., 0.], [0., 0., 1.],
                                                     [0., 1., 0.], [1., 0., 0.],
                                                     [0., 1., 1.], [1., 0., 1.],
                                                     [1., 1., 0.], [1., 1.,
                                                                    1.]])
        else:
            self.deformed_control_points = deformed_control_points
 
        self.power = power
 
    def __call__(self, src_pts):
 
        displ = self.deformed_control_points - self.original_control_points
 
        dist = cdist(src_pts, self.original_control_points, metric='sqeuclidean')
        dist = dist** self.power
 
        # Weights are set as the reciprocal of the distance if the distance is
        # not zero, otherwise 1.0 where distance is zero.
        dist[dist == 0.0] = 1
        weights = 1. / dist
        #weights[dist == 0.0] = 1.0
 
        offset = np.dot(weights, displ) / np.sum(weights, axis=1, keepdims=True)
        return src_pts + offset
 
 
def IDW_cpu(self, srcImg, input_points, output_points):
    start = time.time()
 
    idw = IDW(original_control_points=input_points.astype(np.float64), deformed_control_points=output_points.astype(np.float64), power=3)
 
    h, w = srcImg.shape[:-1]
    x = np.empty((h, w), np.float64)
    x[:, :] = np.arange(w)
    y = np.empty((h, w), np.float64)
    y[:, :] = np.arange(h)[:, np.newaxis]
    mesh = np.array([x.ravel(), y.ravel()])
    mesh = mesh.T
 
    new_mesh = idw(mesh.astype(np.float64))
    UX = new_mesh[:,0].reshape(h,w).astype(np.float32)
    UY = new_mesh[:,1].reshape(h,w).astype(np.float32)
    copyImg = cv2.remap(srcImg, UX, UY, interpolation=cv2.INTER_LINEAR)
 
    end = time.time()
    print("IDW time cost:{} s".format(end - start))
return copyImg

pytorch基于cuda加速实现：

好处，基于最佳cpu版本实现，基于pytorch实现加速，速度快的一逼。缺点，图片太大，注意显存开销。解决思路，使用pytorch1.8以上版本，进行显存设置。当然也可以考虑tensorflow基于静态图的优化。

torch.cuda.set_per_process_memory_fraction(0.5, 0)
参数1：fraction 限制的上限比例，如0.5 就是总GPU显存的一半，可以是0~1的任意float大小；
参数2：device 设备号； 如0 表示GPU卡 0号；

class IDW_TORCH(object):
    def __init__(self,
                 original_control_points=None,
                 deformed_control_points=None,
                 power=1):
 
        if torch.cuda.is_available():
            device = "cuda"
        else:
            device = "cpu"
        self.original_control_points = original_control_points.to(device)
 
        self.deformed_control_points = deformed_control_points.to(device)
 
        self.power = power
        self.device = device
 
    def __call__(self, src_pts):
 
        src_pts = src_pts.to(self.device)
        displ = self.deformed_control_points - self.original_control_points
 
        dist = torch.cdist(src_pts, self.original_control_points)
 
        dist = dist ** (self.power*2)
 
        # Weights are set as the reciprocal of the distance if the distance is
        # not zero, otherwise 1.0 where distance is zero.
        dist[dist == 0.0] = 1
        weights = 1. / dist
 
        offset = torch.matmul(weights, displ) / torch.sum(weights, axis=1, keepdims=True)
        return src_pts + offset
 
def IDW_torch(self, srcImg, input_points, output_points):
    start = time.time()
    idw = IDW_TORCH(original_control_points=torch.from_numpy(input_points.astype(np.float32)),
          deformed_control_points=torch.from_numpy(output_points.astype(np.float32)),
          power=3)
 
    h, w = srcImg.shape[:-1]
    x = torch.empty((h, w))
    x[:, :] = torch.arange(w)
    y = torch.empty((h, w))
    y[:, :] = torch.arange(h)[:, np.newaxis]
    #mesh = torch.vstack([x.flatten(), y.flatten()]).T
    mesh = torch.stack([x.flatten(), y.flatten()], dim=1)
 
    new_mesh = idw(mesh.float()).cpu().numpy()
 
 
    UX = new_mesh[:,0].reshape(h,w).astype(np.float32)
    UY = new_mesh[:,1].reshape(h,w).astype(np.float32)
 
 
    self.idwUX = UX
    self.idwUY = UY
 
    copyImg = cv2.remap(srcImg, UX, UY, interpolation=cv2.INTER_LINEAR)
 
    end = time.time()
    print("IDW TORCH time cost:{} s".format(end - start))
return copyImg

上面所有代码 input_points, output_points，2个矩阵的维度都是(n,2)，n表示点的个数。坐标就是n个点的x,y坐标。只需要拿到人脸图片上，变换前的坐标位置，变换后的坐标位置，调用上面的函数就可以。生成图片基于opencv自带函数cv2.remap，更加高效。

大眼瘦脸运行效果：