We Keep Coding

Labeling a matrix

I've been trying to do a code that labels a binary matrix, i.e. I want to do a function that finds all connected components in an image and assigns a unique label to all points in the same component. The problem is that I found a function, imbinarize(), that creates a binary image and I want to know how to do it without that function (because I don't know how to do it).
EDIT: I realized that it isn't needed to binarize the image, because it is being assumed that all the images that are put as argument are already binarized. So, I changed my code. It happens that code is not working, and I think the problem is in one of the cycles, but I can't understand why.
import numpy as np
%matplotlib inline
from matplotlib import pyplot as plt
def connected_components(image):
M = image * 1
# write your code here
(row, column) = M.shape #shape of the matrix
#Second step
L = 2
#Third step
q = []
#Fourth step
#Method to look for ones starting on the pixel (0, 0) and going from left to right and top-down
for i in np.arange(row):
for j in np.arange(column):
if M[i][j] == 1:
M[i][j] = L
q.append(M[i-1][j])
q.append(M[i+1][j])
q.append(M[i][j-1])
q.append(M[i][j+1])
#Fifth step
while len(q) != 0: #same as saying 'while q is not empty'
if q[0] == 1:
M[0] = L
q.append(M[i-1][j])
q.append(M[i+1][j])
q.append(M[i][j-1])
q.append(M[i][j+1])
#Sixth step
L = L + 1
#Seventh step: goes to the beginning of the for-cycle
return labels

pyplot.binarize in its most simple form thresholds an image such that any intensity whose value is beyond a certain threshold is assigned a binary 1 / True and a binary 0 / False otherwise. It is actually more sophisticated than this as it uses some image morphology for noise removal as well as use adaptive thresholds to find the most optimal value to separate between foreground and background. As I see this post as more for validating the connected components algorithm you've created, I'm going to assume that the basic algorithm is fine and the actual algorithm to be out of scope for your needs.
Once you read in the image with matplotlib, it is most likely going to be three channels so you'll need to convert the image into grayscale first, then threshold after. We can make this more adaptive based on the number of channels that exist.
Therefore, let's define a function to threshold the image for us. You'll need to play around with the threshold until you get good results. Also take note that plt.imread reads in float32 values, so the threshold will be defined between [0-1]. We can try 0.5 as a good start:
def binarize(im, threshold=0.5):
if len(im.shape) == 3:
gray = 0.299*im[...,0] + 0.587*im[...,1] + 0.114*im[...,2]
else:
gray = im
return (gray >= threshold).astype(np.uint8)
This will check if the input image is in RGB. If it is, convert to grayscale accordingly. The method to convert from RGB to grayscale uses the SMPTE Rec. 709 standard. Once we have the grayscale image, simply return a new image where everything that meets the threshold and beyond gets assigned an integer 1 and everything else is integer 0. I've converted the result to an integer type because your connected components algorithm assumes a 0/1 labelling.
You can then replace your code with:
#First step
Image = plt.imread(image) #reads the image on the argument
M = binarize(Image) #imbinarize() converts an image to a binary matrix
(row, column) = np.M.shape #shape of the matrix
Minor Note
In your test code, you are supplying a test image directly whereas your actual code performs an imread operation. imread expects a string so by specifying the actual array, your code will produce an error. If you want to accommodate for both an array and a string, you should check to see if the input is a string vs. an array:
if type(image) is str:
Image = plt.imread(image) #reads the image on the argument
else:
Image = image
M = binarize(Image) #imbinarize() converts an image to a binary matrix
(row, column) = np.M.shape #shape of the matrix

Search for all templates using scikit-image

I am trying to follow the tutorial from scikit-image regarding Template Matching (check it here).
Using just this example, I would like to find all matching coins (maxima) in the image, not only this one which gave the highest score. I was thinking about using:
maxima = argrelextrema(result, np.greater)
but the problem is that it finds also very small local maxima, which are just a noise. Is there any way to screen numpy array and find the strongest maxima? Thanks!

To find all the coins the documentation suggests "...you should use a proper peak-finding function." The easiest of these is probably peak_local_max (as suggested in the comments) which is also from skimage, and has a manual page here. Using some reasonable numbers in the *args gets the peaks out of the response image.
The second comment about the peaks being displaced is also discussed in the documentation
"Note that the peaks in the output of match_template correspond to the origin (i.e. top-left corner) of the template."
One can manually correct for this (by translating the peaks by the side lengths of the template), or you can set the pad_input bool to True (source), which as a by-product means that the peaks in the response function line up with the center of the template at the point of maximal overlap.
Combining these two bits into a script we get something like:
import numpy as np
import matplotlib.pyplot as plt
from skimage import data
from skimage.feature import match_template
from skimage.feature import peak_local_max # new import!
image = data.coins()
coin = image[170:220, 75:130]
result = match_template(image, coin,pad_input=True) #added the pad_input bool
peaks = peak_local_max(result,min_distance=10,threshold_rel=0.5) # find our peaks
# produce a plot equivalent to the one in the docs
plt.imshow(result)
# highlight matched regions (plural)
plt.plot(peaks[:,1], peaks[:,0], 'o', markeredgecolor='r', markerfacecolor='none', markersize=10)

I have been digging and found some solution but unfortunately I am not sure if I know what exactly is done in the script. I have slightly modified script found here:
neighborhood_size = 20 #how many pixels
threshold = 0.01 #threshold of maxima?
data_max = filters.maximum_filter(result, neighborhood_size)
maxima = (result == data_max)
data_min = filters.minimum_filter(result, neighborhood_size)
diff = ((data_max - data_min) > threshold)
maxima[diff == 0] = 0
x_image,y_image = [], []
temp_size = coin.shape[0]
labeled, num_objects = ndimage.label(maxima)
slices = ndimage.find_objects(labeled)
x, y = [], []
for dy,dx in slices:
x_center = (dx.start + dx.stop - 1)/2
x.append(x_center)
y_center = (dy.start + dy.stop - 1)/2
y.append(y_center)
fig, (raw,found) = plt.subplots(1,2)
raw.imshow(image,cmap=plt.cm.gray)
raw.set_axis_off()
found.imshow(result)
found.autoscale(False)
found.set_axis_off()
plt.plot(x,y, 'ro')
plt.show()
and does this:
I also realized, that coordinates of found peaks are shifted in comparison to raw image. I think the difference comes from the template size. I will update when I will find out more.
EDIT: with slight code modification I was able also to find places on the input image:
x_image_center = (dx.start + dx.stop - 1 + temp_size) / 2
x_image.append(x_image_center)
y_image_center = (dy.start + dy.stop - 1 + temp_size) / 2
y_image.append(y_image_center)

local histogram equalization in matlab / python

i am very new in matlab. i want to write the code for local histogram equalization . i have been written code for global histogram equalization and i know that local equalization means do equalization for each part of image seperately but my question is that how i should choose this part of images ? for example should i do equalization for each 100 pixel that are neighbor separate of other pixels ? in the other word how i can take apart image to some parts and then do equalization to each part?

The most naive way to do what you ask is split up your image into non-overlapping blocks, do your global histogram code on that block and save it to the output. Suppose you defined the rows and columns of these non-overlapping blocks as the variables rows and cols. In your case, let's say it's 100 x 100, so rows = 100; cols = 100;. You would simply loop over each non-overlapping block, do your histogram equalization then set this to the same locations in the output.
Something like this below, assuming your image is stored in im:
rows = 100;
cols = 100;
out = zeros(size(im)); % Declare output variable
for ii = 1 : rows : size(im, 1)
for jj = 1 : cols : size(im, 2)
% Get the block
row_begin = ii;
row_end = min(size(im, 1), ii + rows);
col_begin = jj;
col_end = min(size(im, 2), jj + cols);
blk = im(row_begin : row_end, col_begin : col_end, :);
% Perform histogram equalization with the block stored in blk
% ...
% Assume the output of this is stored in O
out(row_begin : row_end, col_begin : col_end, :) = O;
end
end
Note the intricacy of the variable blk that stores the non-overlapping block. We let the beginning row and column simply be the loop counter ii and jj, but the ending row and column we must make sure that it's bounded by the dimensions of the image. That's why the min call is there. Otherwise, the ending row and column is simply the beginning row and column added by the size of the block in the corresponding dimensions. Also note that I've used : to index into the third dimension in case you have a colour image. Grayscale should not affect this code. You finally need to use the same indexing when storing the output in the output image. Note that I've assumed this is stored in the variable O which is the output of your customized histogram equalization function.
The output out will contain your locally histogram equalized image. Take note that you could theoretically do this in one line using blockproc in the image processing toolbox if you have it. This processes distinct blocks in your image and applies some function to it. Assuming your histogram equalization function is called hsteq, you would simply do this:
rows = 100; cols = 100;
out = blockproc(im, [rows, cols], #(s) hsteq(s.data));
The first input is the image you want to process, the second input defines the block size and finally the last element is the function you want to apply to each block. Note that blockproc supplies a customized structure into your function and so what is important is that you pull out the data field in the structure. This should produce the same output as the code above with loops.

We can use the tile-based local (adaptive) histogram equalization to implement AHE (as suggested in the other answer), but in that case we need to implement a bilinear interpolation-like technique to prevent sudden change of contrasts at the edges of the window, e.g., observe the equalized output below with python implementation of the same (here a 50x50 window is used for the tile):
def AHE(im, tile_x=8, tile_y=8):
h, w = im.shape
out = np.zeros(im.shape) # Declare output variable
for i in range(0, h, tile_x):
for j in range(0, w, tile_y):
# Get the block
blk = im[i: min(i + tile_x, h), j: min(j + tile_y, w)]
probs = get_distr(blk)
out[i: min(i + tile_x, h), j: min(j + tile_y, w)] = CHE(blk, probs)
return out
def CHE(im, probs):
T = np.array(list(map(int, 255*np.cumsum(probs))))
return T[im]
def get_distr(im):
hist, _ = np.histogram(im.flatten(),256,[0,256])
return hist / hist.sum()
We could instead implement the AHE algorithm from this thesis:
The implementation of algorithm yields better results (without the boundary artifacts):

Numpy image slicing returning black patches/ wrong values

The end goal is to take an image and slice it up into samples that I save. The problem is that my slices are randomly returning black/ incorrect patches. Bellow is a small sample program.
import scipy.ndimage as ndimage
import scipy.misc as misc
import numpy as np
image32 = misc.imread("work0.png")
patches = np.zeros((36, 8, 8))
for i in range(4):
for j in range(4):
patches[i*4 + j] = image32[i:i+8,j:j+8]
misc.imsave("{0}{1}.png".format(i,j), patches[i*4 + j])
An example of my image would be:
Patch of 0,0 of 8x8 patch yields:

Two things:
You are initializing your patch matrix to be the wrong data type. By default, numpy will make patches matrix a np.float64 type and if you use this with saving, you won't get the results you would expect. Specifically, if you consult Mr. F's answer, there is actually some scaling performed on floating-point images where the minimum and maximum values of the image get scaled to black and white respectively and so if you have an image that is completely uniform in background, both the minimum and maximum will be the same and will get visualized to black. As such, the best thing is to respect the original image's data type, namely setting the dtype of your patches matrix to np.uint8.
Judging from your for loop indexing, you want to extract out 8 x 8 patches that are non-overlapping. This means that if you have a 32 x 32 image with 8 x 8 patches, you have 16 patches in total arranged in a 4 x 4 grid.
Therefore, you need to change the patches statement so that it has 16 in the first dimension, not 36. In addition, you'll have to adjust the way you're indexing into your image to extract out the 8 x 8 patches because right now, the patches are overlapping. Specifically, you want to make the image patch indexing go from 8*i to 8*(i+1) for the rows and 8*j to 8*(j+1) for the columns. If you substitute sample values of i and j yourself, you'll see that we get unique 8 x 8 patches for each grid in your image.
With both of the above things I noted, the modified code should be:
import scipy.ndimage as ndimage
import scipy.misc as misc
import numpy as np
image32 = misc.imread('work0.png')
patches = np.zeros((16,8,8), dtype=np.uint8) # Change
for i in range(4):
for j in range(4):
patches[i*4 + j] = image32[8*i:8*(i+1),8*j:8*(j+1)] # Change
misc.imsave("{0}{1}.png".format(i,j), patches[i*4 + j])
When I do this and take a look at the output images, I get what I expect.
To be absolutely sure, let's plot the segments using matplotlib. You've conveniently saved all of the patches in patches so it shouldn't be a problem showing what we need. However, I'll place some code in comments so that you can read in the images that were saved from disk with your above code so you can verify that it still works, regardless of looking at patches or the images on disk:
import matplotlib.pyplot as plt
plt.figure()
for i in range(4):
for j in range(4):
plt.subplot(4, 4, 4*i + j + 1)
img = patches[4*i + j]
# or you can do this:
# img = misc.imread('{0}{1}.png'.format(i,j))
img = np.dstack([img, img, img])
plt.imshow(img)
plt.show()
The weird thing about matplotlib.pyplot.imshow is that if you have an image that is single channel (such as your case) that has the same intensity all around, it gets visualized to black no matter what the colour map is, much like what we experienced with imsave. Therefore, I had to artificially make this a RGB image but with all of the channels to be the same so this gets visualized as grayscale before we show the image.
We get:

According to this answer the issue is that imsave normalizes the data so that the computed minimum is defined as black (and, if there is a distinct maximum, that is defined as white).
This led me to go digging as to why the suggested use of uint8 did work to create the desired output. As it turns out, in the source there is a function called bytescale that gets called internally.
Actually, imsave itself is a very thin wrapper around toimage followed by save (from the image object). Inside of toimage if mode is None (which it is by default), that's when bytescale gets invoked.
It turns out that bytescale has an if statement that checks for the uint8 data type, and if the data is in that format, it returns the data unaltered. But if not, then the data is scaled according to a max and min transformation (where 0 and 255 are the default low and high pixel values to compare to).
This is the full snippet of code linked above:
if data.dtype == uint8:
return data
if high < low:
raise ValueError("`high` should be larger than `low`.")
if cmin is None:
cmin = data.min()
if cmax is None:
cmax = data.max()
cscale = cmax - cmin
if cscale < 0:
raise ValueError("`cmax` should be larger than `cmin`.")
elif cscale == 0:
cscale = 1
scale = float(high - low) / cscale
bytedata = (data * 1.0 - cmin) * scale + 0.4999
bytedata[bytedata > high] = high
bytedata[bytedata < 0] = 0
return cast[uint8](bytedata) + cast[uint8](low)
For the blocks of your data that are all 255, cscale will be 0, which will be checked for and changed to 1. Then the line
bytedata = (data * 1.0 - cmin) * scale + 0.4999
will result in the whole image block having the float value of 0.4999, thus set explicitly to 0 in the next chunk of code (when casted to uint8 from float) as for example:
In [102]: np.cast[np.uint8](0.4999)
Out[102]: array(0, dtype=uint8)
You can see in the body of bytescale that there are only two possible ways to return: either your data is type uint8 and it's returned as-is, or else it goes through this kind of silly scaling process. So in the end, it is indeed correct, and good practice, to be using uint8 for the pieces of your code that specifically load from or save to an image format via these functions.
So this cascade of stuff is why you were getting all zeros in the outputted image file and why the other suggestion of using dtype=np.uint8 actually helps you. It's not because you need to avoid floating point data for images, just because of this bizarre convention to check and scale data on the part of imsave.

Correct method and Python package that can find width of an image's feature

The input is a spectrum with colorful (sorry) vertical lines on a black background. Given the approximate x coordinate of that band (as marked by X), I want to find the width of that band.
I am unfamiliar with image processing. Please direct me to the correct method of image processing and a Python image processing package that can do the same.
I am thinking PIL, OpenCV gave me an impression of being overkill for this particular application.
What if I want to make this an expert system that can classify them in the future?

I'll give a complete minimal working example (as suggested by sega_sai). I don't have access to your original image, but you'll see it doesn't really matter! The peak distributions found by the code below are:
Mean values at: 26.2840960523 80.8255092125
import Image
from scipy import *
from scipy.optimize import leastsq
# Load the picture with PIL, process if needed
pic = asarray(Image.open("band2.png"))
# Average the pixel values along vertical axis
pic_avg = pic.mean(axis=2)
projection = pic_avg.sum(axis=0)
# Set the min value to zero for a nice fit
projection /= projection.mean()
projection -= projection.min()
# Fit function, two gaussians, adjust as needed
def fitfunc(p,x):
return p[0]*exp(-(x-p[1])**2/(2.0*p[2]**2)) + \
p[3]*exp(-(x-p[4])**2/(2.0*p[5]**2))
errfunc = lambda p, x, y: fitfunc(p,x)-y
# Use scipy to fit, p0 is inital guess
p0 = array([0,20,1,0,75,10])
X = xrange(len(projection))
p1, success = leastsq(errfunc, p0, args=(X,projection))
Y = fitfunc(p1,X)
# Output the result
print "Mean values at: ", p1[1], p1[4]
# Plot the result
from pylab import *
subplot(211)
imshow(pic)
subplot(223)
plot(projection)
subplot(224)
plot(X,Y,'r',lw=5)
show()

Below is a simple thresholding method to find the lines and their width, it should work quite reliably for any number of lines. The yellow and black image below was processed using this script, the red/black plot illustrates the found lines using parameters of threshold = 0.3, min_line_width = 5)
The script averages the rows of an image, and then determines the basic start and end positions of each line based on a threshold (which you can set between 0 and 1), and a minimum line width (in pixels). By using thresholding and minimum line width you can easily filter your input images to get the lines out of them. The first function find_lines returns all the lines in an image as a list of tuples containing the start, end, center, and width of each line. The second function find_closest_band_width is called with the specified x_position, and returns the width of the closest line to this position (assuming you want distance to centre for each line). As the lines are saturated (255 cut-off per channel), their cross-sections are not far from a uniform distribution, so I don't believe trying to fit any kind of distribution is really going to help too much, just unnecessarily complicates.
import Image, ImageStat
def find_lines(image_file, threshold, min_line_width):
im = Image.open(image_file)
width, height = im.size
hist = []
lines = []
start = end = 0
for x in xrange(width):
column = im.crop((x, 0, x + 1, height))
stat = ImageStat.Stat(column)
## normalises by 2 * 255 as in your example the colour is yellow
## if your images start using white lines change this to 3 * 255
hist.append(sum(stat.sum) / (height * 2 * 255))
for index, value in enumerate(hist):
if value > threshold and end >= start:
start = index
if value < threshold and end < start:
if index - start < min_line_width:
start = 0
else:
end = index
center = start + (end - start) / 2.0
width = end - start
lines.append((start, end, center, width))
return lines
def find_closest_band_width(x_position, lines):
distances = [((value[2] - x_position) ** 2) for value in lines]
index = distances.index(min(distances))
return lines[index][3]
## set your threshold, and min_line_width for finding lines
lines = find_lines("8IxWA_sample.png", 0.7, 4)
## sets x_position to 59th pixel
print 'width of nearest line:', find_closest_band_width(59, lines)

I don't think that you need anything fancy for you particular task.
I would just use PIL + scipy. That should be enough.
Because you essentially need to take your image, make a 1D-projection of it
and then fit a Gaussian or something like that to it. The information about the approximate location of the band should be used a first guess for the fitter.