Training Neural Networks with Very Little Data -- A Draft径向变换

最近有一篇针对数据增强的文章比较有意思：这里只讲一下核心的代码实现以及实现细节，原文可以自行查阅：
Training Neural Networks with Very Little Data – A Draft
文章的大概意思就是通过某种变换，将笛卡尔坐标系的图像通过坐标变换，变换成极坐标系下的图像，该变换直接通过下面的公式给出：

变换比较简单，公式也写的很清楚，根据公式实现的代码：
github：
https://github.com/zhly0/radial-transform

from skimage import data
from skimage import io
import numpy as np
import math
import matplotlib.pyplot as plt

def to_gray(img):
    w, h,_ = img.shape
    ret = np.empty((w, h), dtype=np.uint8)
    retf = np.empty((w, h), dtype=np.float)
    imgf = img.astype(float)
    retf[:, :] = ((imgf[:, :, 1] + imgf[:, :, 2] + imgf[:, :, 0])/3)
    ret = retf.astype(np.uint8)
    return ret

def radia_transform(img,w,h):
    shape = im.shape

    new_im = np.zeros(shape)
    print(shape)
    print(len(shape))
    print('w',w)
    print('h',h)
    width = shape[1]
    height = shape[0]
    lens = len(shape)
    for i in range(0,width):
        xita = 2*3.14159*i/width
        for a in range(0,height):
            x = (int)(math.floor(a * math.cos(xita)))
            y = (int)(math.floor(a * math.sin(xita)))
            new_y = (int)(h+x)
            new_x = (int)(w+y)
            #print(h.dtype)
            if new_x>=0 and new_xif new_y>=0 and new_yif lens==3:
                        new_im[a,i,0] = (im[new_y,new_x,0]-127.5)/128
                        new_im[a,i,1] = (im[new_y,new_x,1]-127.5)/128
                        new_im[a,i,2] = (im[new_y,new_x,2]-127.5)/128
                    else:
                        new_im[a,i] = (im[new_y,new_x]-127.5)/128
                        new_im[a,i] = (im[new_y,new_x]-127.5)/128
                        new_im[a,i] = (im[new_y,new_x]-127.5)/128
    return new_im

im = io.imread('E:/1.jpg')
im = to_gray(im)
h = im.shape[0]
w = im.shape[1]

new_im1 = radia_transform(im,(int)(w/2),(int)(h/2))

new_im2 = radia_transform(im,(int)(w/4),(int)(h/4))

new_im3 = radia_transform(im,(int)(w*0.5),(int)(h*0.75))


plt.figure(num='astronaut',figsize=(8,8))  

plt.subplot(2,2,1)     
plt.title('origin image')  
plt.imshow(im,plt.cm.gray)      

plt.subplot(2,2,2)    
plt.title('0.5')  
plt.imshow(new_im1,plt.cm.gray)     
plt.axis('off')    

plt.subplot(2,2,3)    
plt.title('0.25')  
plt.imshow(new_im2,plt.cm.gray)     
plt.axis('off')    

plt.subplot(2,2,4)    
plt.title('0.75')  
plt.imshow(new_im3,plt.cm.gray)     
plt.axis('off')     

plt.show()  

以及对应的变换：