Develop Reference

Unable to increase the region of interest of an image

I am trying to increase the region of interest of an image using the below algorithm.
First, the set of pixels of the exterior border of the ROI is de termined, i.e., pixels that are outside the ROI and are neighbors (using four-neighborhood) to pixels inside it. Then, each pixel value of this set is replaced with the mean value of its neighbors (this time using eight-neighborhood) inside the ROI. Finally, the ROI is expanded by inclusion of this altered set of pixels. This process is repeated and can be seen as artificially increasing the ROI.
The pseudocode is below -
while there are border pixels:
border_pixels = []
# find the border pixels
for each pixel p=(i, j) in image
if p is not in ROI and ((i+1, j) in ROI or (i-1, j) in ROI or (i, j+1) in ROI or (i, j-1) in ROI) or (i-1,j-1) in ROI or (i+1,j+1) in ROI):
add p to border_pixels
# calculate the averages
for each pixel p in border_pixels:
color_sum = 0
count = 0
for each pixel n in 8-neighborhood of p:
if n in ROI:
color_sum += color(n)
count += 1
color(p) = color_sum / count
# update the ROI
for each pixel p=(i, j) in border_pixels:
set p to be in ROI
Below is my code
img = io.imread(path_dir)
newimg = np.zeros((584, 565,3))
mask = img == 0
while(1):
border_pixels = []
for i in range(img.shape[0]):
for j in range(img.shape[1]):
for k in range(0,3):
if(i+1<=583 and j+1<=564 and i-1>=0 and j-1>=0):
if ((mask[i][j][k]) and ((mask[i+1][j][k]== False) or (mask[i-1][j][k]==False) or (mask[i][j+1][k]==False) or (mask[i][j-1][k]==False) or (mask[i-1][j-1][k] == False) or(mask[i+1][j+1][k]==False))):
border_pixels.append([i,j,k])
if len(border_pixels) == 0:
break
for (each_i,each_j,each_k) in border_pixels:
color_sum = 0
count = 0
eight_neighbourhood = [[each_i-1,each_j],[each_i+1,each_j],[each_i,each_j-1],[each_i,each_j+1],[each_i-1,each_j-1],[each_i-1,each_j+1],[each_i+1,each_j-1],[each_i+1,each_j+1]]
for pix_i,pix_j in eight_neighbourhood:
if (mask[pix_i][pix_j][each_k] == False):
color_sum+=img[pix_i,pix_j,each_k]
count+=1
print(color_sum//count)
img[each_i][each_j][each_k]=(color_sum//count)
for (i,j,k) in border_pixels:
mask[i,j,k] = False
border_pixels.remove([i,j,k])
io.imsave("tryout6.png",img)
But it is not doing any change in the image.I am getting the same image as before
so I tried plotting the border pixel on a black image of the same dimension for the first iteration and I am getting the below result-
I really don't have any idea where I am doing wrong here.

Here's a solution that I think works as you have requested (although I agree with #Peter Boone that it will take a while). My implementation has a triple loop, but maybe someone else can make it faster!
First, read in the image. With my method, the pixel values are floats between 0 and 1 (rather than integers between 0 and 255).
import urllib
import matplotlib.pyplot as plt
import numpy as np
from skimage.morphology import binary_dilation, binary_erosion, disk
from skimage.color import rgb2gray
from skimage.filters import threshold_otsu
# create a file-like object from the url
f = urllib.request.urlopen("https://i.stack.imgur.com/JXxJM.png")
# read the image file in a numpy array
# note that all pixel values are between 0 and 1 in this image
a = plt.imread(f)
Second, add some padding around the edges, and threshold the image. I used Otsu's method, but #Peter Boone's answer works well, too.
# add black padding around image 100 px wide
a = np.pad(a, ((100,100), (100,100), (0,0)), mode = "constant")
# convert to greyscale and perform Otsu's thresholding
grayscale = rgb2gray(a)
global_thresh = threshold_otsu(grayscale)
binary_global1 = grayscale > global_thresh
# define number of pixels to expand the image
num_px_to_expand = 50
The image, binary_global1 is a mask that looks like this:
Since the image is three channels (RGB), I process the channels separately. I noticed that I needed to erode the image by ~5 px because the outside of the image has some unusual colors and patterns.
# process each channel (RGB) separately
for channel in range(a.shape[2]):
# select a single channel
one_channel = a[:, :, channel]
# reset binary_global for the each channel
binary_global = binary_global1.copy()
# erode by 5 px to get rid of unusual edges from original image
binary_global = binary_erosion(binary_global, disk(5))
# turn everything less than the threshold to 0
one_channel = one_channel * binary_global
# update pixels one at a time
for jj in range(num_px_to_expand):
# get 1 px ring of to update
px_to_update = np.logical_xor(binary_dilation(binary_global, disk(1)),
binary_global)
# update those pixels with the average of their neighborhood
x, y = np.where(px_to_update == 1)
for x, y in zip(x,y):
# make 3 x 3 px slices
slices = np.s_[(x-1):(x+2), (y-1):(y+2)]
# update a single pixel
one_channel[x, y] = (np.sum(one_channel[slices]*
binary_global[slices]) /
np.sum(binary_global[slices]))
# update original image
a[:,:, channel] = one_channel
# increase binary_global by 1 px dilation
binary_global = binary_dilation(binary_global, disk(1))
When I plot the output, I get something like this:
# plot image
plt.figure(figsize=[10,10])
plt.imshow(a)

This is an interesting idea. You're going to want to use masks and some form of mean ranks to accomplish this. Going pixel by pixel will take you a while, instead you want to use different convolution filters.
If you do something like this:
image = io.imread("roi.jpg")
mask = image[:,:,0] < 30
just_inside = binary_dilation(mask) ^ mask
image[~just_inside] = [0,0,0]
you will have a mask representing just the pixels inside of the ROI. I also set the pixels not in that area to 0,0,0.
Then you can get the pixels just outside of the roi:
just_outside = binary_erosion(mask) ^ mask
Then get the mean bilateral of each channel:
mean_blue = mean_bilateral(image[:,:,0], selem=square(3), s0=1, s1=255)
#etc...
This isn't exactly correct, but I think it should put you in the right direction. I would check out image.sc if you have more general questions about image processing. Let me know if you need more help as this was more general direction than working code.

How to remove a rough line artifact from image after binarization

I am stuck in a problem where I want to differentiate between an object and the background(having a semi-transparent white sheet with backlight) i.e a fixed rough line introduced in the background and is merged with the object. My algorithm right now is I am taking the image from the camera, smoothing with gaussian blur, then extracting Value component from HSV, applying local binarization using wolf method to get the binarized image after which using OpenCV connected component algorithm I remove some small artifacts that are not connected to object as seen here. Now there is only this line artifact which is merged with the object but I want only the object as seen in this image. Please note that there are 2 lines in the binary image so using the 8 connected logic to detect lines not making a loop is not possible this is what I think and tried also. here is the code for that
size = np.size(thresh_img)
skel = np.zeros(thresh_img.shape,np.uint8)
element = cv2.getStructuringElement(cv2.MORPH_RECT,(3,3))
done = False
while( not done):
eroded = cv2.erode(thresh_img,element)
temp = cv2.dilate(eroded,element)
temp = cv2.subtract(thresh_img,temp)
skel = cv2.bitwise_or(skel,temp)
thresh_img = eroded.copy()
zeros = size - cv2.countNonZero(thresh_img)
if zeros==size:
done = True
# set max pixel value to 1
s = np.uint8(skel > 0)
count = 0
i = 0
while count != np.sum(s):
# non-zero pixel count
count = np.sum(s)
# examine 3x3 neighborhood of each pixel
filt = cv2.boxFilter(s, -1, (3, 3), normalize=False)
# if the center pixel of 3x3 neighborhood is zero, we are not interested in it
s = s*filt
# now we have pixels where the center pixel of 3x3 neighborhood is non-zero
# if a pixels' 8-connectivity is less than 2 we can remove it
# threshold is 3 here because the boxfilter also counted the center pixel
s[s < 1] = 0
# set max pixel value to 1
s[s > 0] = 1
i = i + 1
Any help in the form of code would be highly appreciated thanks.

Since you are already using connectedComponents the best way is to exclude, not only the ones which are small, but also the ones that are touching the borders of the image.
You can know which ones are to be discarded using connectedComponentsWithStats() that gives you also information about the bounding box of each component.
Alternatively, and very similarly you can switch from connectedComponents() to findContours() which gives you directly the Components so you can discard the external ones and the small ones to retrieved the part you are interested in.

How to efficiently initialize parts of an array with numpy?

I am trying to figure out if I can use numpy to efficiently set a region of a 3 dimensional array to a value. My array is a black image with 3 color channels and I want to set a region around a set of pixels in the image to a certain color.
My working, but slow, code is something like this (extracted relevant portions):
import skimage
import numpy as np
def clamp(n, upper, lower=0):
return max(lower, min(n, upper))
def apply_contours(image, contours, color=(128.0,128.0,128.0), radius=5):
"""Draw the pixels in the contours in a given colour and size
"""
for contour in contours:
for pixel in contour:
r1 = clamp(int(pixel[0])-radius, image.shape[0])
r2 = clamp(int(pixel[0])+radius, image.shape[0])
c1 = clamp(int(pixel[1])-radius, image.shape[1])
c2 = clamp(int(pixel[1])+radius, image.shape[1])
for y in range(r1,r2):
for x in range(c1,c2):
for c in range(3):
image[y][x][c] = color[c]
return image
input = skimage.io.imread("image.png")
contours = skimage.measure.find_contours(input, 0.5)
mask = np.zeros((input.shape[0],input.shape[1],3), dtype=np.uint8)
apply_contours(mask)
I've not used numpy much but it occurred to me that I should be able speed this up by replacing the nested loop in apply_contours with something like this:
image[r1:r2][c1:c2] = np.array([color[0],color[1],color[2])
but this doesn't seem to work as the resulting image does show any change, where as with the loop version it shows what I'm expecting.
I also tried:
image[r1:r2][c1:c2][0] = color[0]
image[r1:r2][c1:c2][1] = color[1]
image[r1:r2][c1:c2][2] = color[2]
but this gives me an error IndexError: index 0 is out of bounds for axis 0 with size 0.
Is it possible to do what I'm trying to do more efficiently with numpy?

I figured it out, my total n00b status with numpy. The correct syntax is:
image[r1:r2,c1:c2] = np.array([color[0],color[1],color[2])

Detect if an OCR text image is upside down

I have some hundreds of images (scanned documents), most of them are skewed. I wanted to de-skew them using Python.
Here is the code I used:
import numpy as np
import cv2
from skimage.transform import radon
filename = 'path_to_filename'
# Load file, converting to grayscale
img = cv2.imread(filename)
I = cv2.cvtColor(img, COLOR_BGR2GRAY)
h, w = I.shape
# If the resolution is high, resize the image to reduce processing time.
if (w > 640):
I = cv2.resize(I, (640, int((h / w) * 640)))
I = I - np.mean(I) # Demean; make the brightness extend above and below zero
# Do the radon transform
sinogram = radon(I)
# Find the RMS value of each row and find "busiest" rotation,
# where the transform is lined up perfectly with the alternating dark
# text and white lines
r = np.array([np.sqrt(np.mean(np.abs(line) ** 2)) for line in sinogram.transpose()])
rotation = np.argmax(r)
print('Rotation: {:.2f} degrees'.format(90 - rotation))
# Rotate and save with the original resolution
M = cv2.getRotationMatrix2D((w/2,h/2),90 - rotation,1)
dst = cv2.warpAffine(img,M,(w,h))
cv2.imwrite('rotated.jpg', dst)
This code works well with most of the documents, except with some angles: (180 and 0) and (90 and 270) are often detected as the same angle (i.e it does not make difference between (180 and 0) and (90 and 270)). So I get a lot of upside-down documents.
Here is an example:
The resulted image that I get is the same as the input image.
Is there any suggestion to detect if an image is upside down using Opencv and Python?
PS: I tried to check the orientation using EXIF data, but it didn't lead to any solution.
EDIT:
It is possible to detect the orientation using Tesseract (pytesseract for Python), but it is only possible when the image contains a lot of characters.
For anyone who may need this:
import cv2
import pytesseract
print(pytesseract.image_to_osd(cv2.imread(file_name)))
If the document contains enough characters, it is possible for Tesseract to detect the orientation. However, when the image has few lines, the orientation angle suggested by Tesseract is usually wrong. So this can not be a 100% solution.

Python3/OpenCV4 script to align scanned documents.
Rotate the document and sum the rows. When the document has 0 and 180 degrees of rotation, there will be a lot of black pixels in the image:
Use a score keeping method. Score each image for it's likeness to a zebra pattern. The image with the best score has the correct rotation. The image you linked to was off by 0.5 degrees. I omitted some functions for readability, the full code can be found here.
# Rotate the image around in a circle
angle = 0
while angle <= 360:
# Rotate the source image
img = rotate(src, angle)
# Crop the center 1/3rd of the image (roi is filled with text)
h,w = img.shape
buffer = min(h, w) - int(min(h,w)/1.15)
roi = img[int(h/2-buffer):int(h/2+buffer), int(w/2-buffer):int(w/2+buffer)]
# Create background to draw transform on
bg = np.zeros((buffer*2, buffer*2), np.uint8)
# Compute the sums of the rows
row_sums = sum_rows(roi)
# High score --> Zebra stripes
score = np.count_nonzero(row_sums)
scores.append(score)
# Image has best rotation
if score <= min(scores):
# Save the rotatied image
print('found optimal rotation')
best_rotation = img.copy()
k = display_data(roi, row_sums, buffer)
if k == 27: break
# Increment angle and try again
angle += .75
cv2.destroyAllWindows()
How to tell if the document is upside down? Fill in the area from the top of the document to the first non-black pixel in the image. Measure the area in yellow. The image that has the smallest area will be the one that is right-side-up:
# Find the area from the top of page to top of image
_, bg = area_to_top_of_text(best_rotation.copy())
right_side_up = sum(sum(bg))
# Flip image and try again
best_rotation_flipped = rotate(best_rotation, 180)
_, bg = area_to_top_of_text(best_rotation_flipped.copy())
upside_down = sum(sum(bg))
# Check which area is larger
if right_side_up < upside_down: aligned_image = best_rotation
else: aligned_image = best_rotation_flipped
# Save aligned image
cv2.imwrite('/home/stephen/Desktop/best_rotation.png', 255-aligned_image)
cv2.destroyAllWindows()

Assuming you did run the angle-correction already on the image, you can try the following to find out if it is flipped:
Project the corrected image to the y-axis, so that you get a 'peak' for each line. Important: There are actually almost always two sub-peaks!
Smooth this projection by convolving with a gaussian in order to get rid of fine structure, noise, etc.
For each peak, check if the stronger sub-peak is on top or at the bottom.
Calculate the fraction of peaks that have sub-peaks on the bottom side. This is your scalar value that gives you the confidence that the image is oriented correctly.
The peak finding in step 3 is done by finding sections with above average values. The sub-peaks are then found via argmax.
Here's a figure to illustrate the approach; A few lines of you example image
Blue: Original projection
Orange: smoothed projection
Horizontal line: average of the smoothed projection for the whole image.
here's some code that does this:
import cv2
import numpy as np
# load image, convert to grayscale, threshold it at 127 and invert.
page = cv2.imread('Page.jpg')
page = cv2.cvtColor(page, cv2.COLOR_BGR2GRAY)
page = cv2.threshold(page, 127, 255, cv2.THRESH_BINARY_INV)[1]
# project the page to the side and smooth it with a gaussian
projection = np.sum(page, 1)
gaussian_filter = np.exp(-(np.arange(-3, 3, 0.1)**2))
gaussian_filter /= np.sum(gaussian_filter)
smooth = np.convolve(projection, gaussian_filter)
# find the pixel values where we expect lines to start and end
mask = smooth > np.average(smooth)
edges = np.convolve(mask, [1, -1])
line_starts = np.where(edges == 1)[0]
line_endings = np.where(edges == -1)[0]
# count lines with peaks on the lower side
lower_peaks = 0
for start, end in zip(line_starts, line_endings):
line = smooth[start:end]
if np.argmax(line) < len(line)/2:
lower_peaks += 1
print(lower_peaks / len(line_starts))
this prints 0.125 for the given image, so this is not oriented correctly and must be flipped.
Note that this approach might break badly if there are images or anything not organized in lines in the image (maybe math or pictures). Another problem would be too few lines, resulting in bad statistics.
Also different fonts might result in different distributions. You can try this on a few images and see if the approach works. I don't have enough data.

You can use the Alyn module. To install it:
pip install alyn
Then to use it to deskew images(Taken from the homepage):
from alyn import Deskew
d = Deskew(
input_file='path_to_file',
display_image='preview the image on screen',
output_file='path_for_deskewed image',
r_angle='offest_angle_in_degrees_to_control_orientation')`
d.run()
Note that Alyn is only for deskewing text.

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.