如何根据对象位置旋转图像?

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【中文标题】如何根据对象位置旋转图像?【英文标题】:How can I rotate an image based on object position? 【发布时间】:2021-07-18 01:39:49 【问题描述】:

首先,很抱歉帖子的长度。

我正在开展一个基于叶子图像对植物进行分类的项目。为了减少数据的方差,我需要旋转图像,使茎在图像底部水平对齐(270 度)。

我目前所处的位置...

到目前为止,我所做的是创建一个阈值图像,然后从那里找到轮廓并在对象周围绘制一个椭圆(在许多情况下,它无法涉及整个对象,因此省略了茎...),之后即,我创建了 4 个区域(带有椭圆的边缘)并尝试计算最小值区域,这是由于假设在这些点中的任何一个都必须找到茎,因此它将是人口较少的区域(主要是因为它会被 0 包围),这显然不是我想要的。

之后我以两种不同的方式计算旋转的角度,第一种涉及atan2函数,这只需要我想要移动的点(人口最少区域的质心)和@ 987654403@ 和y = height。这种方法在某些情况下有效,但在大多数情况下,我没有得到所需的角度,有时需要一个负角度,它会产生一个正角度,最后是顶部的茎。在其他一些情况下,它只是以可怕的方式失败。

我的第二种方法是尝试根据 3 个点计算角度:图像中心、人口最少区域的质心和 270º 点。然后使用arccos 函数,并将其结果转换为度数。

这两种方法对我来说都失败了。

问题

您认为这是一种正确的方法还是我只是让事情变得比我应该做的更复杂? 如何找到叶子的茎(这不是可选的,它必须是茎)?因为我的想法不太好...... 如何以稳健的方式确定角度?由于第二个问题的相同原因...

这里有一些样本和我得到的结果(二进制掩码)。矩形表示我正在比较的区域,椭圆上的红线是椭圆的长轴,粉红色圆圈是最小区域内的质心,红色圆圈表示 270º 参考点(角度) ,白点代表图像的中心。

我目前的解决方案

    def brightness_distortion(I, mu, sigma):
        return np.sum(I*mu/sigma**2, axis=-1) / np.sum((mu/sigma)**2, axis=-1)
    
    
    def chromacity_distortion(I, mu, sigma):
        alpha = brightness_distortion(I, mu, sigma)[...,None]
        return np.sqrt(np.sum(((I - alpha * mu)/sigma)**2, axis=-1))
    
    def bwareafilt ( image ):
        image = image.astype(np.uint8)
        nb_components, output, stats, centroids = cv2.connectedComponentsWithStats(image, connectivity=4)
        sizes = stats[:, -1]
    
        max_label = 1
        max_size = sizes[1]
        for i in range(2, nb_components):
            if sizes[i] > max_size:
                max_label = i
                max_size = sizes[i]
    
        img2 = np.zeros(output.shape)
        img2[output == max_label] = 255
    
        return img2
    
    def get_thresholded_rotated(im_path):
        
        #read image
        img = cv2.imread(im_path)
        
        img = cv2.resize(img, (600, 800), interpolation = Image.BILINEAR)
        
        sat = cv2.cvtColor(img, cv2.COLOR_BGR2HSV)[:,:,1]
        val = cv2.cvtColor(img, cv2.COLOR_BGR2HSV)[:,:,2]
        sat = cv2.medianBlur(sat, 11)
        val = cv2.medianBlur(val, 11)
        
        #create threshold
        thresh_S = cv2.adaptiveThreshold(sat , 255, cv2.ADAPTIVE_THRESH_MEAN_C, cv2.THRESH_BINARY, 401, 10);
        thresh_V = cv2.adaptiveThreshold(val , 255, cv2.ADAPTIVE_THRESH_MEAN_C, cv2.THRESH_BINARY, 401, 10);
        
        #mean, std
        mean_S, stdev_S = cv2.meanStdDev(img, mask = 255 - thresh_S)
        mean_S = mean_S.ravel().flatten()
        stdev_S = stdev_S.ravel()
        
        #chromacity
        chrom_S = chromacity_distortion(img, mean_S, stdev_S)
        chrom255_S = cv2.normalize(chrom_S, chrom_S, alpha=0, beta=255, norm_type=cv2.NORM_MINMAX).astype(np.uint8)[:,:,None]
        
        mean_V, stdev_V = cv2.meanStdDev(img, mask = 255 - thresh_V)
        mean_V = mean_V.ravel().flatten()
        stdev_V = stdev_V.ravel()
        chrom_V = chromacity_distortion(img, mean_V, stdev_V)
        chrom255_V = cv2.normalize(chrom_V, chrom_V, alpha=0, beta=255, norm_type=cv2.NORM_MINMAX).astype(np.uint8)[:,:,None]
        
        #create different thresholds
        thresh2_S = cv2.adaptiveThreshold(chrom255_S , 255, cv2.ADAPTIVE_THRESH_MEAN_C, cv2.THRESH_BINARY, 401, 10);
        thresh2_V = cv2.adaptiveThreshold(chrom255_V , 255, cv2.ADAPTIVE_THRESH_MEAN_C, cv2.THRESH_BINARY, 401, 10);
            
    
        #thresholded image
        thresh = cv2.bitwise_and(thresh2_S, cv2.bitwise_not(thresh2_V))
        
        #find countours and keep max
        contours = cv2.findContours(thresh, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)
        contours = contours[0] if len(contours) == 2 else contours[1]
        big_contour = max(contours, key=cv2.contourArea)
            
        # fit ellipse to leaf contours
        ellipse = cv2.fitEllipse(big_contour)
        (xc,yc), (d1,d2), angle = ellipse
        
        print('thresh shape: ', thresh.shape)
        #print(xc,yc,d1,d2,angle)
        
        rmajor = max(d1,d2)/2
        
        rminor = min(d1,d2)/2
        
        origi_angle = angle
        
        if angle > 90:
            angle = angle - 90
        else:
            angle = angle + 90
            
        #calc major axis line
        xtop = xc + math.cos(math.radians(angle))*rmajor
        ytop = yc + math.sin(math.radians(angle))*rmajor
        xbot = xc + math.cos(math.radians(angle+180))*rmajor
        ybot = yc + math.sin(math.radians(angle+180))*rmajor
        
        #calc minor axis line
        xtop_m = xc + math.cos(math.radians(origi_angle))*rminor
        ytop_m = yc + math.sin(math.radians(origi_angle))*rminor
        xbot_m = xc + math.cos(math.radians(origi_angle+180))*rminor
        ybot_m = yc + math.sin(math.radians(origi_angle+180))*rminor
        
        #determine which region is up and which is down
        if max(xtop, xbot) == xtop :
            x_tij = xtop
            y_tij = ytop
            
            x_b_tij = xbot
            y_b_tij = ybot
        else:
            x_tij = xbot
            y_tij = ybot
            
            x_b_tij = xtop
            y_b_tij = ytop
            
        
        if max(xtop_m, xbot_m) == xtop_m :
            x_tij_m = xtop_m
            y_tij_m = ytop_m
            
            x_b_tij_m = xbot_m
            y_b_tij_m = ybot_m
        else:
            x_tij_m = xbot_m
            y_tij_m = ybot_m
            
            x_b_tij_m = xtop_m
            y_b_tij_m = ytop_m
            
            
        print('-----')
        print(x_tij, y_tij)
        

        rect_size = 100
        
        """
        calculate regions of edges of major axis of ellipse
        this is done by creating a squared region of rect_size x rect_size, being the edge the center of the square
        """
        x_min_tij = int(0 if x_tij - rect_size < 0 else x_tij - rect_size)
        x_max_tij = int(thresh.shape[1]-1 if x_tij + rect_size > thresh.shape[1] else x_tij + rect_size)
        
        y_min_tij = int(0 if y_tij - rect_size < 0 else y_tij - rect_size)
        y_max_tij = int(thresh.shape[0] - 1 if y_tij + rect_size > thresh.shape[0] else y_tij + rect_size)
      
        
        x_b_min_tij = int(0 if x_b_tij - rect_size < 0 else x_b_tij - rect_size)
        x_b_max_tij = int(thresh.shape[1] - 1 if x_b_tij + rect_size > thresh.shape[1] else x_b_tij + rect_size)
        
        y_b_min_tij = int(0 if y_b_tij - rect_size < 0 else y_b_tij - rect_size)
        y_b_max_tij = int(thresh.shape[0] - 1 if y_b_tij + rect_size > thresh.shape[0] else y_b_tij + rect_size)
        
    
        sum_red_region =   np.sum(thresh[y_min_tij:y_max_tij, x_min_tij:x_max_tij])
    
        sum_yellow_region =   np.sum(thresh[y_b_min_tij:y_b_max_tij, x_b_min_tij:x_b_max_tij])
        
        
        """
        calculate regions of edges of minor axis of ellipse
        this is done by creating a squared region of rect_size x rect_size, being the edge the center of the square
        """
        x_min_tij_m = int(0 if x_tij_m - rect_size < 0 else x_tij_m - rect_size)
        x_max_tij_m = int(thresh.shape[1]-1 if x_tij_m + rect_size > thresh.shape[1] else x_tij_m + rect_size)
        
        y_min_tij_m = int(0 if y_tij_m - rect_size < 0 else y_tij_m - rect_size)
        y_max_tij_m = int(thresh.shape[0] - 1 if y_tij_m + rect_size > thresh.shape[0] else y_tij_m + rect_size)
      
        
        x_b_min_tij_m = int(0 if x_b_tij_m - rect_size < 0 else x_b_tij_m - rect_size)
        x_b_max_tij_m = int(thresh.shape[1] - 1 if x_b_tij_m + rect_size > thresh.shape[1] else x_b_tij_m + rect_size)
        
        y_b_min_tij_m = int(0 if y_b_tij_m - rect_size < 0 else y_b_tij_m - rect_size)
        y_b_max_tij_m = int(thresh.shape[0] - 1 if y_b_tij_m + rect_size > thresh.shape[0] else y_b_tij_m + rect_size)
        
        #value of the regions, the names of the variables are related to the color of the rectangles drawn at the end of the function
        sum_red_region_m =   np.sum(thresh[y_min_tij_m:y_max_tij_m, x_min_tij_m:x_max_tij_m])
    
        sum_yellow_region_m =   np.sum(thresh[y_b_min_tij_m:y_b_max_tij_m, x_b_min_tij_m:x_b_max_tij_m])
        
     
        #print(sum_red_region, sum_yellow_region, sum_red_region_m, sum_yellow_region_m)
        
        
        min_arg = np.argmin(np.array([sum_red_region, sum_yellow_region, sum_red_region_m, sum_yellow_region_m]))
        
        print('min: ', min_arg)
           
        
        if min_arg == 1: #sum_yellow_region < sum_red_region :
            
            
            left_quartile = x_b_tij < thresh.shape[0] /2 
            upper_quartile = y_b_tij < thresh.shape[1] /2
    
            center_x = x_b_min_tij + ((x_b_max_tij - x_b_min_tij) / 2)
            center_y = y_b_min_tij + (y_b_max_tij - y_b_min_tij / 2)
            
    
            center_x = x_b_min_tij + np.argmax(thresh[y_b_min_tij:y_b_max_tij, x_b_min_tij:x_b_max_tij].mean(axis=0))
            center_y = y_b_min_tij + np.argmax(thresh[y_b_min_tij:y_b_max_tij, x_b_min_tij:x_b_max_tij].mean(axis=1))
    
        elif min_arg == 0:
            
            left_quartile = x_tij < thresh.shape[0] /2 
            upper_quartile = y_tij < thresh.shape[1] /2
    
    
            center_x = x_min_tij + ((x_b_max_tij - x_b_min_tij) / 2)
            center_y = y_min_tij + ((y_b_max_tij - y_b_min_tij) / 2)
    
            
            center_x = x_min_tij + np.argmax(thresh[y_min_tij:y_max_tij, x_min_tij:x_max_tij].mean(axis=0))
            center_y = y_min_tij + np.argmax(thresh[y_min_tij:y_max_tij, x_min_tij:x_max_tij].mean(axis=1))
            
        elif min_arg == 3:
            
            
            left_quartile = x_b_tij_m < thresh.shape[0] /2 
            upper_quartile = y_b_tij_m < thresh.shape[1] /2
    
            center_x = x_b_min_tij_m + ((x_b_max_tij_m - x_b_min_tij_m) / 2)
            center_y = y_b_min_tij_m + (y_b_max_tij_m - y_b_min_tij_m / 2)
            
    
            center_x = x_b_min_tij_m + np.argmax(thresh[y_b_min_tij_m:y_b_max_tij_m, x_b_min_tij_m:x_b_max_tij_m].mean(axis=0))
            center_y = y_b_min_tij_m + np.argmax(thresh[y_b_min_tij_m:y_b_max_tij_m, x_b_min_tij_m:x_b_max_tij_m].mean(axis=1))
    
        else:
            
            left_quartile = x_tij_m < thresh.shape[0] /2 
            upper_quartile = y_tij_m < thresh.shape[1] /2
    
    
            center_x = x_min_tij_m + ((x_b_max_tij_m - x_b_min_tij_m) / 2)
            center_y = y_min_tij_m + ((y_b_max_tij_m - y_b_min_tij_m) / 2)
            
            center_x = x_min_tij_m + np.argmax(thresh[y_min_tij_m:y_max_tij_m, x_min_tij_m:x_max_tij_m].mean(axis=0))
            center_y = y_min_tij_m + np.argmax(thresh[y_min_tij_m:y_max_tij_m, x_min_tij_m:x_max_tij_m].mean(axis=1))
            
        # draw ellipse on copy of input
        result = img.copy() 
        cv2.ellipse(result, ellipse, (0,0,255), 1)

        cv2.line(result, (int(xtop),int(ytop)), (int(xbot),int(ybot)), (255, 0, 0), 1)
        cv2.circle(result, (int(xc),int(yc)), 10, (255, 255, 255), -1)
    
        cv2.circle(result, (int(center_x),int(center_y)), 10, (255, 0, 255), 5)
    
        cv2.circle(result, (int(thresh.shape[1] / 2),int(thresh.shape[0] - 1)), 10, (255, 0, 0), 5)
    
        cv2.rectangle(result,(x_min_tij,y_min_tij),(x_max_tij,y_max_tij),(255,0,0),3)
        cv2.rectangle(result,(x_b_min_tij,y_b_min_tij),(x_b_max_tij,y_b_max_tij),(255,255,0),3)
        
        cv2.rectangle(result,(x_min_tij_m,y_min_tij_m),(x_max_tij_m,y_max_tij_m),(255,0,0),3)
        cv2.rectangle(result,(x_b_min_tij_m,y_b_min_tij_m),(x_b_max_tij_m,y_b_max_tij_m),(255,255,0),3)
        
       
        plt.imshow(result)
        plt.figure()
        #rotate the image    
        rot_img = Image.fromarray(thresh)
            
        #180
        bot_point_x = int(thresh.shape[1] / 2)
        bot_point_y = int(thresh.shape[0] - 1)
        
        #poi
        poi_x = int(center_x)
        poi_y = int(center_y)
        
        #image_center
        im_center_x = int(thresh.shape[1] / 2)
        im_center_y = int(thresh.shape[0] - 1) / 2
        
        #a - adalt, b - abaix, c - dreta
        #ba = a - b
        #bc = c - a(b en realitat) 
        
        ba = np.array([im_center_x, im_center_y]) - np.array([bot_point_x, bot_point_y])
        bc = np.array([poi_x, poi_y]) - np.array([im_center_x, im_center_y])
        
        #angle 3 punts    
        cosine_angle = np.dot(ba, bc) / (np.linalg.norm(ba) * np.linalg.norm(bc))
        cos_angle = np.arccos(cosine_angle)
        
        cos_angle = np.degrees(cos_angle)
        
        print('cos angle: ', cos_angle)
        
        print('print: ', abs(poi_x- bot_point_x))
        
        m = (int(thresh.shape[1] / 2)-int(center_x) / int(thresh.shape[0] - 1)-int(center_y))
        
        ttan = math.tan(m)
        
        theta = math.atan(ttan)
            
        print('theta: ', theta) 
        
        result = Image.fromarray(result)
        
        result = result.rotate(cos_angle)
        
        plt.imshow(result)
        plt.figure()
    
        #rot_img = rot_img.rotate(origi_angle)
    
        rot_img = rot_img.rotate(cos_angle)
    
        return rot_img
    
    
    rot_img = get_thresholded_rotated(im_path)
    
    plt.imshow(rot_img)

提前致谢 --- 编辑 ---

我根据要求在这里留下了一些原始图像。

sample

【问题讨论】:

这是一个有趣的问题,我希望我有时间来解决它。因此,假设您制作了一个边界椭圆,甚至是一个边界圆。假设您将那个圆圈分成两部分(在许多不同的旋转中)。对于某些旋转,一半的像素强度将远高于另一半的强度。如果你找到一个使两半之间的比率最大化的分割,那么强度较低的一半就是茎部分。明白我的意思了吗? 您可能甚至不需要边界圆。对于从 0 到 359 的每个度数,取一条穿过图像中心的线,并将线两边的像素相加。那很容易。好的,不是“容易”,而是可行的。这只是数学,对吧? ;) 一条评论。我认为您应该使用 inRange 而不是自适应阈值对绿色进行阈值处理。您的一些阈值图像包含无关部分。 您可以先将图像水平分成两半,然后再垂直分成两半,然后检查绿色的数量。绿色像素数量最少的那个可能包含您的茎。 fmw42,我可以在 inRange 中使用绿色阈值,我可能会这样做,但我希望传入的图像(这是为了对用户发布到服务器的图像进行分类)具有任何类型的背景而不是一张白纸,这就是我使用自适应阈值的原因 【参考方案1】:

Bilateral Symmetry

旋转图像。找到最大的轮廓。使用矩,找到该轮廓的中心。将图像分成左右两部分(注意:应用cv2.blur(img, 5,5)) 会产生更好的效果):

翻转右侧。左右叠加:

使用 cv2.absDiff() 测量左侧和(翻转)右侧之间的差异。由于叶子具有左右对称性,当叶子的茎(或刺)垂直时差异最小。

注意:会有两个最小值;当茎向上时一次,当茎向下时一次......

【讨论】:

哈哈,看了你的回答,看了动画,心想:“就是他*!”然后,我向下滚动,然后 - 是你! :D 错过了你的动画! (*假设这里是名字的代词。) 嗨斯蒂芬,谢谢你的回答。我只是想实现它。当我找到质心(矩)时,这显然不是图像的中心,所以左右大小不同,这是叠加图像的问题。 @M.Villanueva 我也遇到了这个问题!我的解决方案是使用相同大小的临时图像,然后将它们与 cv2.addWeighted() 混合。代码不是很漂亮......但它有效。所有相关像素都在图像的右侧,所以我裁剪了图像的左侧。【参考方案2】:

概念

这适用于大多数叶子,只要它们有茎。所以这里是检测和旋转一张叶子图像的旋转的概念:

    找到叶子的近似轮廓。由于茎的尖端通常属于叶子的凸包(外部点),因此找到轮廓的凸包。

    遍历属于叶子凸包的轮廓索引。对于每个索引,计算3个点之间的角度:索引之前的轮廓中的点,索引处的轮廓中的点和索引之后的轮廓中的点。

    计算的最小角度将是茎的尖端。每次循环找到一个较小的角度,将三个点存储在一个元组中,当检测到最小的角度时,使用尖端两侧的2个坐标的中心计算茎指向的角度茎和茎的尖端。

    检测到茎的角度后,我们可以相应地旋转图像。

代码

import cv2
import numpy as np

def process(img):
    img_gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
    img_blur = cv2.GaussianBlur(img_gray, (3, 3), 2)
    img_canny = cv2.Canny(img_blur, 127, 47)
    kernel = np.ones((5, 5))
    img_dilate = cv2.dilate(img_canny, kernel, iterations=2)
    img_erode = cv2.erode(img_dilate, kernel, iterations=1)
    return img_erode

def get_contours(img):
    contours, _ = cv2.findContours(process(img), cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_NONE)
    cnt = max(contours, key=cv2.contourArea)
    peri = cv2.arcLength(cnt, True)
    return cv2.approxPolyDP(cnt, 0.01 * peri, True)

def get_angle(a, b, c):
    ba, bc = a - b, c - b
    cos_angle = np.dot(ba, bc) / (np.linalg.norm(ba) * np.linalg.norm(bc))
    return np.degrees(np.arccos(cos_angle))
    
def get_rot_angle(img):
    contours = get_contours(img)
    length = len(contours)
    min_angle = 180
    for i in cv2.convexHull(contours, returnPoints=False).ravel():
        a, b, c = contours[[i - 1, i, (i + 1) % length], 0]
        angle = get_angle(a, b, c)
        if angle < min_angle:
            min_angle = angle
            pts = a, b, c
    a, b, c = pts
    return 180 - np.degrees(np.arctan2(*(np.mean((a, c), 0) - b)))

def rotate(img):
    h, w, _ = img.shape
    rot_mat = cv2.getRotationMatrix2D((w / 2, h / 2), get_rot_angle(img), 1)
    return cv2.warpAffine(img, rot_mat, (w, h), flags=cv2.INTER_LINEAR)

img = cv2.imread("leaf.jpg")
cv2.imshow("Image", rotate(img))
cv2.waitKey(0)

输出

您提供的每个示例图像的输出:

解释

分解代码:

    导入必要的库:
import cv2
import numpy as np
    定义一个函数process,将图像处理成二值图像,从而使程序能够准确检测树叶的轮廓:
def process(img):
    img_gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
    img_blur = cv2.GaussianBlur(img_gray, (3, 3), 2)
    img_canny = cv2.Canny(img_blur, 127, 47)
    kernel = np.ones((5, 5))
    img_dilate = cv2.dilate(img_canny, kernel, iterations=2)
    img_erode = cv2.erode(img_dilate, kernel, iterations=1)
    return img_erode
    定义一个函数get_contours,获取图像中最大轮廓的近似轮廓,使用之前定义的process函数:
def get_contours(img):
    contours, _ = cv2.findContours(process(img), cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_NONE)
    cnt = max(contours, key=cv2.contourArea)
    peri = cv2.arcLength(cnt, True)
    return cv2.approxPolyDP(cnt, 0.01 * peri, True)
    定义一个函数get_angle,获取3点之间的角度:
def get_angle(a, b, c):
    ba, bc = a - b, c - b
    cos_angle = np.dot(ba, bc) / (np.linalg.norm(ba) * np.linalg.norm(bc))
    return np.degrees(np.arccos(cos_angle))
    定义一个函数get_rot_angle,以获取图像需要旋转的度数。它通过使用前面定义的get_angle 函数找到叶子凸包的点来确定该角度,在该点与叶子轮廓中的 2 个周围点之间的角度最小,其中 3 个点之间的角度最小:
def get_rot_angle(img):
    contours = get_contours(img)
    length = len(contours)
    min_angle = 180
    for i in cv2.convexHull(contours, returnPoints=False).ravel():
        a, b, c = contours[[i - 1, i, (i + 1) % length], 0]
        angle = get_angle(a, b, c)
        if angle < min_angle:
            min_angle = angle
            pts = a, b, c
    a, b, c = pts
    return 180 - np.degrees(np.arctan2(*(np.mean((a, c), 0) - b)))
    定义一个函数rotate,使用之前定义的get_rot_angle 函数沿其中心旋转图像:
def rotate(img):
    h, w, _ = img.shape
    rot_mat = cv2.getRotationMatrix2D((w / 2, h / 2), get_rot_angle(img), 1)
    return cv2.warpAffine(img, rot_mat, (w, h), flags=cv2.INTER_LINEAR)
    最后,读入图像,应用之前定义的rotate 函数并显示旋转后的图像:
img = cv2.imread("leaf.jpg")
cv2.imshow("Image", rotate(img))
cv2.waitKey(0)

【讨论】:

非常感谢,这种方法在大多数情况下都解决了问题(正如您所指出的),也感谢您的出色解释。【参考方案3】:

这就是我的意思,这需要改进。这会沿着顶部边缘每 5 个像素绘制一条穿过图像中心的假想线,然后沿着左边缘每 5 个像素绘制一条假想线,将线两侧的像素值相加,并打印最小和最大比率。元组的第四个值应该是旋转的角度。

from PIL import Image
import numpy as np
import math
from pprint import pprint

def rads(degs):
    return degs * math.pi / 180.0

clr = Image.open('20210210_155311.jpg').resize((640,480)).convert('L')
data = np.asarray(clr)


def ratio_lr( data, left, right ):
    x0 = left
    dx = (right-left) / data.shape[0]

    lsum = 0
    rsum = 0
    for row in range(data.shape[0]):
        lsum += data[row,:int(x0)].sum()
        rsum += data[row,int(x0):].sum()
        x0 += dx

    return lsum / rsum

def ratio_tb( data, top, bottom ):
    y0 = top
    dy = (bottom - top) / data.shape[1]

    tsum = 0
    bsum = 0
    for col in range(data.shape[1]):
        tsum += data[:int(y0),col].sum()
        bsum += data[int(y0):,col].sum()
        y0 += dy

    return tsum / bsum


midx = data.shape[1] // 2
midy = data.shape[0] // 2
track = []
for dx in range(-midx, midx, 5 ):
    if dx == 0:
        angle = 90
    else:
        angle = math.atan( midy / dx  ) * 180 / math.pi
    track.append( (ratio_lr( data, midx+dx, midx-dx ), dx, 0, angle) )

for dy in range(-midy, midy, 5 ):
    angle = math.atan( dy / midx ) * 180 / math.pi
    track.append((ratio_tb( data, midy+dy, midy-dy ), 0, dy, angle))

pprint(track)
print(min(track))
print(max(track))

【讨论】:

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