Develop Reference

Extract most central area in a Binary Image

I am processing binary images, and was previously using this code to find the largest area in the binary image:
# Use the hue value to convert to binary
thresh = 20
thresh, thresh_img = cv2.threshold(h, thresh, 255, cv2.THRESH_BINARY)
cv2.imshow('thresh', thresh_img)
cv2.waitKey(0)
cv2.destroyAllWindows()
# Finding Contours
# Use a copy of the image since findContours alters the image
contours, _ = cv2.findContours(thresh_img.copy(), cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_NONE)
#Extract the largest area
c = max(contours, key=cv2.contourArea)
This code isn't really doing what I need it to do, now I think it would better to extract the most central area in the binary image.
Binary Image
Largest Image
This is currently what the code is extracting, but I am hoping to get the central circle in the first binary image extracted.

OpenCV comes with a point-polygon test function (for contours). It even gives a signed distance, if you ask for that.
I'll find the contour that is closest to the center of the picture. That may be a contour actually overlapping the center of the picture.
Timings, on my quadcore from 2012, give or take a millisecond:
findContours: ~1 millisecond
all pointPolygonTests and argmax: ~1 millisecond
mask = cv.imread("fkljm.png", cv.IMREAD_GRAYSCALE)
(height, width) = mask.shape
ret, mask = cv.threshold(mask, 128, 255, cv.THRESH_BINARY) # required because the sample picture isn't exactly clean
# get contours
contours, hierarchy = cv.findContours(mask, cv.RETR_LIST | cv.RETR_EXTERNAL, cv.CHAIN_APPROX_SIMPLE)
center = (np.array([width, height]) - 1) / 2
# find contour closest to center of picture
distances = [
cv.pointPolygonTest(contour, center, True) # looking for most positive (inside); negative is outside
for contour in contours
]
iclosest = np.argmax(distances)
print("closest contour is", iclosest, "with distance", distances[iclosest])
# draw closest contour
canvas = cv.cvtColor(mask, cv.COLOR_GRAY2BGR)
cv.drawContours(image=canvas, contours=[contours[iclosest]], contourIdx=-1, color=(0, 255, 0), thickness=5)
closest contour is 45 with distance 65.19202405202648
a cv.floodFill() on the center point can also quickly yield a labeling on that blob... assuming the mask is positive there. Otherwise, there needs to be search.
(cx, cy) = center.astype(int)
assert mask[cy,cx], "floodFill not applicable"
# trying cv.floodFill on the image center
mask2 = mask >> 1 # turns everything else gray
cv.floodFill(image=mask2, mask=None, seedPoint=center.astype(int), newVal=255)
# use (mask2 == 255) to identify that blob
This also takes less than a millisecond.
Some practically faster approaches might involve a pyramid scheme (low-res versions of the mask) to quickly identify areas of the picture that are candidates for an exact test (distance/intersection).
Test target pixel. Hit (positive)? Done.
Calculate low-res mask. Per block, if any pixel is positive, block is positive.
Find positive blocks, sort by distance, examine closer all those that are within sqrt(2) * blocksize of the best distance.

There are several ways you define "most central." I chose to define it as the region with the closest distance to the point you're searching for. If the point is inside the region, then that distance will be zero.
I also chose to do this with a pixel-based approach rather than a polygon-based approach, like you're doing with findContours().
Here's a step-by-step breakdown of what this code is doing.
Load the image, put it into grayscale, and threshold it. You're already doing these things.
Identify connected components of the image. Connected components are places where there are white pixels which are directly connected to other white pixels. This breaks up the image into regions.
Using np.argwhere(), convert a true/false mask into an array of coordinates.
For each coordinate, compute the Euclidean distance between that point and search_point.
Find the minimum within each region.
Across all regions, find the smallest distance.
import cv2
import numpy as np
img = cv2.imread('test197_img.png')
gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
_, thresh_img = cv2.threshold(gray,127,255,cv2.THRESH_BINARY)
n_groups, comp_grouped = cv2.connectedComponents(thresh_img)
components = []
search_point = [600, 150]
for i in range(1, n_groups):
mask = (comp_grouped == i)
component_coords = np.argwhere(mask)[:, ::-1]
min_distance = np.sqrt(((component_coords - search_point) ** 2).sum(axis=1)).min()
components.append({
'mask': mask,
'min_distance': min_distance,
})
closest = min(components, key=lambda x: x['min_distance'])['mask']
Output:

Rotate incomplete box so it is vertical

I have a dataset of x-ray images that i am trying to clean by rotating the images so the arm is vertical and cropping the image of any excess space. Here are some examples from the dataset:
I am currently working out the best way to work out the angle of the x-ray and rotate the image based on that.
My curent approach is to detect the line of the side of the rectangle that the scan is in using the hough transform, and rotate the image based on that.
I tried to run the hough transform on the output of a canny edge detector but this doesnt work so well for images where the edge of the rectangle is blurred like in the first image.
I cant use cv's box detection as sometimes the rectangle around the scan has an edge off screen.
So i currently use adaptive thresholding to find the edge of the box and then median filter it and try to find the longest line in this, but sometimes the wrong line is the longest and the image gets rotated completley wrong.
Adaptive thresholding is used due to the fact that soem scans have different brightnesses.
The current implementation i have is:
def get_lines(img):
#threshold
thresh = cv2.adaptiveThreshold(img, 255, cv2.ADAPTIVE_THRESH_GAUSSIAN_C, cv2.THRESH_BINARY_INV, 15, 4.75)
median = cv2.medianBlur(thresh, 3)
# detect lines
lines = cv2.HoughLines(median, 1, np.pi/180, 175)
return sorted(lines, key=lambda x: x[0][0], reverse=True)
def rotate(image, angle):
(h, w) = image.shape[:2]
(cX, cY) = (w // 2, h // 2)
M = cv2.getRotationMatrix2D((cX, cY), angle, 1.0)
cos = np.abs(M[0, 0])
sin = np.abs(M[0, 1])
nW = int((h * sin) + (w * cos))
nH = int((h * cos) + (w * sin))
M[0, 2] += (nW / 2) - cX
M[1, 2] += (nH / 2) - cY
return cv2.warpAffine(image, M, (nW, nH))
def fix_rotation(input):
lines = get_lines(input)
rho, theta = lines[0][0]
return rotate_bound(input, theta*180/np.pi)
and produces the following results:
When it goes wrong:
I was wondering if there are any better techniques to usein order to improve the performance of this and what the best way to go about cropping the images after they have been rotated would be?

The idea is to use the blob of the arm itself and fit an ellipse around it. Then, extract its major axis. I quickly tested the idea in Matlab – not OpenCV. Here's what I did, you should be able to use OpenCV's equivalent functions to achieve similar outputs.
First, compute the threshold value of your input via Otsu. Then add some bias to the threshold value to find a better segmentation and use this value to threshold the image.
In pseudo-code:
//the bias value
threshBias = 0.4;
//get the binary threshold via otsu:
thresholdLevel = graythresh( grayInput, “otsu” );
//add bias to the original value
thresholdLevel = thresholdLevel - threshSensitivity * thresholdLevel;
//get the fixed binary image:
thresholdLevel = imbinarize( grayInput, thresholdLevel );
After small blob filtering, this is the output:
Now, get the contours/blobs and fit an ellipse for each contour. Check out the OpenCV example here: https://docs.opencv.org/3.4.9/de/d62/tutorial_bounding_rotated_ellipses.html
You end up with two ellipses:
We are looking for the biggest ellipse, the one with the biggest area and the biggest major and minor axis. I used the width and height of each ellipse to filter the results. The target ellipse is then colored in green. Finally, I get the major axis of the target ellipse, here colored in yellow:
Now, to implement these ideas in OpenCV you have these options:
Use fitEllipse to find the ellipses. The return value of this
function is a RotatedRect object. The data stored here are the
vertices of the ellipse.
Instead of fitting an ellipse you could try using minAreaRect, which
finds a rotated rectangle of the minimum area enclosing a blob.

You can use image moments to calculate the rotation angle.
Using opencv moments function, calculate the second order central moments to construct a covariance matrix and then obtain the orientation as shown here in the Image moment wiki page.
Obtain the normalized central moments nu20, nu11 and nu02 from opencv moments. Then the orientation is calculated as
0.5 * arctan(2 * nu11/(nu20 - nu02))
Please refer the given link for details.
You can use the raw image itself or the preprocessed one for the calculation of orientation. See which one gives you better accuracy and use it.
As for the bounding-box, once you rotate the image, assuming you used the preprocessed one, get all the non-zero pixel coordinates of the rotated image and calculate their upright bounding-box using opencv boundingRect.

Python OpenCV: Hough Transform does not detect obvious lines

Problem:
I want to detect lines in a given image using OpenCV in Python. Although there are multiple obvious vertical lines, neither normal HoughLines nor probabilistic HoughLines does find them. As I spent plenty of time playing around with the Parameters, I guess I am doing something fundamental wrong here. I am Aware of the fact, that hough-lines is usually applied on edges, e.g. after using canny. Due to canny´s non-maximum supression, canny does not give good results here.
Image, where detecting the vertical lines Fails :
Why:
Given this (image of a water meter) :
I want to detect the rectangle around each digit. To detect the rectangles, I used sobel filters in x and y direction and calculated Magnitude and angle/Phase of the Gradient. As I assume the image to be rotated correctly in this step, I extract vertical and horizontal edges as shown in the image. My hope was to make use of houghLines to find the bounding boxes. Finding the horizontal lines works perfectly, as seen in the
Debug plot containing further insights on the Problem, where as I does not work on the vertical components (second row) :
Detecting the rectangles around each digit would help me to
locate the Region of Interest
cut out the region inside the rectangle, in other words the digit. Several other approches to detect the digits directly by using contours, all had the problem of the outer rectangles interfering with the digit.
Update: the Code for detecting the vertical lines:
#img is initialized with the binarized, vertical component image, as shown above
minLength = 30
maxGap = 7
angle_res = np.pi / 180
rad_res = 2
threshold_val = 100
linesP = cv2.HoughLinesP(img, rad_res, angle_res, threshold_val, minLineLength=minLength, maxLineGap=maxGap)
cdst = cv2.cvtColor(img, cv2.COLOR_GRAY2BGR)
cdstP = np.copy(cdst)
if linesP is None:
print("Error when finding lines (probabilistic hough transformation). No lines detected")
else:
# Copy edges to the images that will display the results in BGR
for i in range(0, len(linesP)):
l = linesP[i][0]
cv2.line(cdstP, (l[0], l[1]), (l[2], l[3]), (255,0,0), 3, cv2.LINE_AA)
plt.imshow(cdstP); plt.show()

First apply canny edge with proper settings of threshold. Then apply probabilistic hough line transform. After applying hough transform filter the lines with slope. You want to filter the box so you need to filter horizontal and vertical lines. After filtering lines apply morphological dilation and erosion operation back to back to resultant image to get neat box around each digit. While applying hough transform select parameters minimum line length, maximum line length and maximum line gap appropriately.
You can use trackbar function while selecting appropriate parameters. The sample code is given below for selection of threshold for canny edge.
import cv2
import numpy as np
cv2.namedWindow('Result')
img = cv2.imread('qkEuE.png')
v1 = 0
v2 = 0
def doEdges():
edges = cv2.Canny(img,v1,v2)
edges = cv2.cvtColor(edges,cv2.COLOR_GRAY2BGR)
res = np.concatenate((img,edges),axis = 0)
cv2.imshow('Result',res)
def setVal1(val):
global v1
v1 = val
doEdges()
def setVal2(val):
global v2
v2 = val
doEdges()
cv2.createTrackbar('Val1','Result',0,500,setVal1)
cv2.createTrackbar('Val2','Result',0,500,setVal2)
cv2.imshow('Result',img)
cv2.waitKey(0)
cv2.destroyAllWindows
Hope it helps you.

finding largest connected component using opencv 2.4 in python 2.7

I am writing code in python 2.7.12 using opencv '2.4.9.1'.
I have a 2d numpy array containing values in range [0,255].
My aim is to find largest region containing value in range[x,y]
I found
How to use python OpenCV to find largest connected component in a single channel image that matches a specific value? as pretty well-explained .
Only, the catch is - it is meant for opencv 3 .
I can try to write a function of this type
[pseudo code]
def get_component(x,y,list):
append x,y to list
visited[x][y]=1
if(x+1<m && visited[x+1][y]==0)
get_component(x+1,y,list)
if(y+1<n && visited[x][y+1]==0)
get_component(x,y+1,list)
if(x+1<m)&&(y+1<n)&&visited[x+1][y+1]==0
get_component(x+1,y+1,list)
return
MAIN
biggest_component = NULL
biggest_component_size = 0
low = lowest_value_in_user_input_range
high = highest_value_in_user_input_range
matrix a = gray image of size mxn
matrix visited = all value '0' of size mxn
for x in range(m):
for y in range(n):
list=NULL
if(a[x][y]>=low) && (a[x][y]<=high) && visited[x][y]==1:
get_component(x,y,list)
if (list.size>biggest_component_size)
biggest_component = list
Get maximum x , maximum y , min x and min y from above list containing coordinates of every point of largest component to make rectangle R .
Mission accomplished !
[/pseudo code]
Such an approach will not be efficient, I think.
Can you suggest functions for doing the same with my setup ?
Thanks.

Happy to see my answer linked! Indeed, connectedComponentsWithStats() and even connectedComponents() are OpenCV 3+ functions, so you can't use them. Instead, the easy thing to do is just use findContours().
You can calculate moments() of each contour, and included in the moments is the area of the contour.
Important note: The OpenCV function findContours() uses 8-way connectivity, not 4-way (i.e. it also checks diagonal connectivity, not just up, down, left, right). If you need 4-way, you'd need to use a different approach. Let me know if that's the case and I can update..
In the spirit of the other post, here's the general approach:
Binarize your image with the thresholds you're interested in.
Run cv2.findContours() to get the contour of each distinct component in the image.
For each contour, calculate the cv2.moments() of the contour and keep the maximum area contour (m00 in the dict returned from moments() is the area of the contour).
Either keep the contour as a list of points if that's what you need, otherwise draw them on a new blank image if you want it as a mask.
I lack creativity today, so you get the cameraman as our example image as you didn't provide one.
import cv2
import numpy as np
img = cv2.imread('cameraman.png', cv2.IMREAD_GRAYSCALE)
Now, let's binarize to get some separated blobs:
bin_img = cv2.inRange(img, 50, 80)
Now let's find the contours.
contours = cv2.findContours(bin_img, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_NONE)[0]
# For OpenCV 3+ use:
# contours = cv2.findContours(bin_img, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_NONE)[1]
Now for the main bit; looping through the contours and finding the largest one:
max_area = 0
max_contour_index = 0
for i, contour in enumerate(contours):
contour_area = cv2.moments(contour)['m00']
if contour_area > max_area:
max_area = contour_area
max_contour_index = i
So now we have an index max_contour_index of the largest contour by area, so you can access the largest contour directly just by doing contours[max_contour_index]. You could of course just sort the contours list by the contour area and grab the first (or last, depending on sort order). If you want to make a mask of the one component, you can use
cv2.drawContours(new_blank_image, contours, max_contour_index, color=255, thickness=-1)
Note the -1 will fill the contour as opposed to outlining it. Here's an example drawing the contour over the original image:
Looks about right.
All in one function:
def largest_component_mask(bin_img):
"""Finds the largest component in a binary image and returns the component as a mask."""
contours = cv2.findContours(bin_img, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_NONE)[0]
# should be [1] if OpenCV 3+
max_area = 0
max_contour_index = 0
for i, contour in enumerate(contours):
contour_area = cv2.moments(contour)['m00']
if contour_area > max_area:
max_area = contour_area
max_contour_index = i
labeled_img = np.zeros(bin_img.shape, dtype=np.uint8)
cv2.drawContours(labeled_img, contours, max_contour_index, color=255, thickness=-1)
return labeled_img

Edge detection for image stored in matrix

I represent images in the form of 2-D arrays. I have this picture:
How can I get the pixels that are directly on the boundaries of the gray region and colorize them?
I want to get the coordinates of the matrix elements in green and red separately. I have only white, black and gray regions on the matrix.

The following should hopefully be okay for your needs (or at least help). The idea is to split into the various regions using logical checks based on threshold values. The edge between these regions can then be detected using numpy roll to shift pixels in x and y and comparing to see if we are at an edge,
import matplotlib.pyplot as plt
import numpy as np
import scipy as sp
from skimage.morphology import closing
thresh1 = 127
thresh2 = 254
#Load image
im = sp.misc.imread('jBD9j.png')
#Get threashold mask for different regions
gryim = np.mean(im[:,:,0:2],2)
region1 = (thresh1<gryim)
region2 = (thresh2<gryim)
nregion1 = ~ region1
nregion2 = ~ region2
#Plot figure and two regions
fig, axs = plt.subplots(2,2)
axs[0,0].imshow(im)
axs[0,1].imshow(region1)
axs[1,0].imshow(region2)
#Clean up any holes, etc (not needed for simple figures here)
#region1 = sp.ndimage.morphology.binary_closing(region1)
#region1 = sp.ndimage.morphology.binary_fill_holes(region1)
#region1.astype('bool')
#region2 = sp.ndimage.morphology.binary_closing(region2)
#region2 = sp.ndimage.morphology.binary_fill_holes(region2)
#region2.astype('bool')
#Get location of edge by comparing array to it's
#inverse shifted by a few pixels
shift = -2
edgex1 = (region1 ^ np.roll(nregion1,shift=shift,axis=0))
edgey1 = (region1 ^ np.roll(nregion1,shift=shift,axis=1))
edgex2 = (region2 ^ np.roll(nregion2,shift=shift,axis=0))
edgey2 = (region2 ^ np.roll(nregion2,shift=shift,axis=1))
#Plot location of edge over image
axs[1,1].imshow(im)
axs[1,1].contour(edgex1,2,colors='r',lw=2.)
axs[1,1].contour(edgey1,2,colors='r',lw=2.)
axs[1,1].contour(edgex2,2,colors='g',lw=2.)
axs[1,1].contour(edgey2,2,colors='g',lw=2.)
plt.show()
Which gives the . For simplicity I've use roll with the inverse of each region. You could roll each successive region onto the next to detect edges
Thank you to #Kabyle for offering a reward, this is a problem that I spent a while looking for a solution to. I tried scipy skeletonize, feature.canny, topology module and openCV with limited success... This way was the most robust for my case (droplet interface tracking). Hope it helps!

There is a very simple solution to this: by definition any pixel which has both white and gray neighbors is on your "red" edge, and gray and black neighbors is on the "green" edge. The lightest/darkest neighbors are returned by the maximum/minimum filters in skimage.filters.rank, and a binary combination of masks of pixels that have a lightest/darkest neighbor which is white/gray or gray/black respectively produce the edges.
Result:
A worked solution:
import numpy
import skimage.filters.rank
import skimage.morphology
import skimage.io
# convert image to a uint8 image which only has 0, 128 and 255 values
# the source png image provided has other levels in it so it needs to be thresholded - adjust the thresholding method for your data
img_raw = skimage.io.imread('jBD9j.png', as_grey=True)
img = numpy.zeros_like(img, dtype=numpy.uint8)
img[:,:] = 128
img[ img_raw < 0.25 ] = 0
img[ img_raw > 0.75 ] = 255
# define "next to" - this may be a square, diamond, etc
selem = skimage.morphology.disk(1)
# create masks for the two kinds of edges
black_gray_edges = (skimage.filters.rank.minimum(img, selem) == 0) & (skimage.filters.rank.maximum(img, selem) == 128)
gray_white_edges = (skimage.filters.rank.minimum(img, selem) == 128) & (skimage.filters.rank.maximum(img, selem) == 255)
# create a color image
img_result = numpy.dstack( [img,img,img] )
# assign colors to edge masks
img_result[ black_gray_edges, : ] = numpy.asarray( [ 0, 255, 0 ] )
img_result[ gray_white_edges, : ] = numpy.asarray( [ 255, 0, 0 ] )
imshow(img_result)
P.S. Pixels which have black and white neighbors, or all three colors neighbors, are in an undefined category. The code above doesn't color those. You need to figure out how you want the output to be colored in those cases; but it is easy to extend the approach above to produce another mask or two for that.
P.S. The edges are two pixels wide. There is no getting around that without more information: the edges are between two areas, and you haven't defined which one of the two areas you want them to overlap in each case, so the only symmetrical solution is to overlap both areas by one pixel.
P.S. This counts the pixel itself as its own neighbor. An isolated white or black pixel on gray, or vice versa, will be considered as an edge (as well as all the pixels around it).

While plonser's answer may be rather straight forward to implement, I see it failing when it comes to sharp and thin edges. Nevertheless, I suggest you use part of his approach as preconditioning.
In a second step you want to use the Marching Squares Algorithm. According to the documentation of scikit-image, it is
a special case of the marching cubes algorithm (Lorensen, William and
Harvey E. Cline. Marching Cubes: A High Resolution 3D Surface
Construction Algorithm. Computer Graphics (SIGGRAPH 87 Proceedings)
21(4) July 1987, p. 163-170
There even exists a Python implementation as part of the scikit-image package. I have been using this algorithm (my own Fortran implementation, though) successfully for edge detection of eye diagrams in communications engineering.
Ad 1: Preconditioning
Create a copy of your image and make it two color only, e.g. black/white. The coordinates remain the same, but you make sure that the algorithm can properly make a yes/no-decision independent from the values that you use in your matrix representation of the image.
Ad 2: Edge Detection
Wikipedia as well as various blogs provide you with a pretty elaborate description of the algorithm in various languages, so I will not go into it's details. However, let me give you some practical advice:
Your image has open boundaries at the bottom. Instead of modifying the algorithm, you can artifically add another row of pixels (black or grey to bound the white/grey areas).
The choice of the starting point is critical. If there are not too many images to be processed, I suggest you select it manually. Otherwise you will need to define rules. Since the Marching Squares Algorithm can start anywhere inside a bounded area, you could choose any pixel of a given color/value to detect the corresponding edge (it will initially start walking in one direction to find an edge).
The algorithm returns the exact 2D positions, e.g. (x/y)-tuples. You can either
iterate through the list and colorize the corresponding pixels by assigning a different value or
create a mask to select parts of your matrix and assign the value that corresponds to a different color, e.g. green or red.
Finally: Some Post-Processing
I suggested to add an artificial boundary to the image. This has two advantages:
1. The Marching Squares Algorithm works out of the box.
2. There is no need to distinguish between image boundary and the interface between two areas within the image. Just remove the artificial boundary once you are done setting the colorful edges -- this will remove the colored lines at the boundary of the image.

Basically by follow pyStarter's suggestion of using the marching square algorithm from scikit-image, the desired could contours can be extracted with the following code:
import matplotlib.pyplot as plt
import numpy as np
import scipy as sp
from skimage import measure
import scipy.ndimage as ndimage
from skimage.color import rgb2gray
from pprint import pprint
#Load image
im = rgb2gray(sp.misc.imread('jBD9j.png'))
n, bins_edges = np.histogram(im.flatten(),bins = 100)
# Skip the black area, and assume two distinct regions, white and grey
max_counts = np.sort(n[bins_edges[0:-1] > 0])[-2:]
thresholds = np.select(
[max_counts[i] == n for i in range(max_counts.shape[0])],
[bins_edges[0:-1]] * max_counts.shape[0]
)
# filter our the non zero values
thresholds = thresholds[thresholds > 0]
fig, axs = plt.subplots()
# Display image
axs.imshow(im, interpolation='nearest', cmap=plt.cm.gray)
colors = ['r','g']
for i, threshold in enumerate(thresholds):
contours = measure.find_contours(im, threshold)
# Display all contours found for this threshold
for n, contour in enumerate(contours):
axs.plot(contour[:,1], contour[:,0],colors[i], lw = 4)
axs.axis('image')
axs.set_xticks([])
axs.set_yticks([])
plt.show()
!
However, from your image there is no clear defined gray region, so I took the two largest counts of intensities in the image and thresholded on these. A bit disturbing is the red region in the middle of the white region, however I think this could be tweaked with the number of bins in the histogram procedure. You could also set these manually as Ed Smith did.

Maybe there is a more elegant way to do that ...
but in case your array is a numpy array with dimensions (N,N) (gray scale) you can do
import numpy as np
# assuming black -> 0 and white -> 1 and grey -> 0.5
black_reg = np.where(a < 0.1, a, 10)
white_reg = np.where(a > 0.9, a, 10)
xx_black,yy_black = np.gradient(black_reg)
xx_white,yy_white = np.gradient(white_reg)
# getting the coordinates
coord_green = np.argwhere(xx_black**2 + yy_black**2>0.2)
coord_red = np.argwhere(xx_white**2 + yy_white**2>0.2)
The number 0.2 is just a threshold and needs to be adjusted.

I think you are probably looking for edge detection method for gray scale images. There are many ways to do that. Maybe this can help http://en.m.wikipedia.org/wiki/Edge_detection. For differentiating edges between white and gray and edges between black and gray, try use local average intensity.