I have a problem with FFT implementation in Python. I have completely strange results.
Ok so, I want to open image, get value of every pixel in RGB, then I need to use fft on it, and convert to image again.
My steps:
1) I'm opening image with PIL library in Python like this
from PIL import Image
im = Image.open("test.png")
2) I'm getting pixels
pixels = list(im.getdata())
3) I'm seperate every pixel to r,g,b values
for x in range(width):
for y in range(height):
r,g,b = pixels[x*width+y]
red[x][y] = r
green[x][y] = g
blue[x][y] = b
4). Let's assume that I have one pixel (111,111,111). And use fft on all red values like this
red = np.fft.fft(red)
And then:
print (red[0][0], green[0][0], blue[0][0])
My output is:
(53866+0j) 111 111
It's completely wrong I think. My image is 64x64, and FFT from gimp is completely different. Actually, my FFT give me only arrays with huge values, thats why my output image is black.
Do you have any idea where is problem?
[EDIT]
I've changed as suggested to
red= np.fft.fft2(red)
And after that I scale it
scale = 1/(width*height)
red= abs(red* scale)
And still, I'm getting only black image.
[EDIT2]
Ok, so lets take one image.
Assume that I dont want to open it and save as greyscale image. So I'm doing like this.
def getGray(pixel):
r,g,b = pixel
return (r+g+b)/3
im = Image.open("test.png")
im.load()
pixels = list(im.getdata())
width, height = im.size
for x in range(width):
for y in range(height):
greyscale[x][y] = getGray(pixels[x*width+y])
data = []
for x in range(width):
for y in range(height):
pix = greyscale[x][y]
data.append(pix)
img = Image.new("L", (width,height), "white")
img.putdata(data)
img.save('out.png')
After this, I'm getting this image , which is ok. So now, I want to make fft on my image before I'll save it to new one, so I'm doing like this
scale = 1/(width*height)
greyscale = np.fft.fft2(greyscale)
greyscale = abs(greyscale * scale)
after loading it. After saving it to file, I have . So lets try now open test.png with gimp and use FFT filter plugin. I'm getting this image, which is correct
How I can handle it?
Great question. I’ve never heard of it but the Gimp Fourier plugin seems really neat:
A simple plug-in to do fourier transform on you image. The major advantage of this plugin is to be able to work with the transformed image inside GIMP. You can so draw or apply filters in fourier space, and get the modified image with an inverse FFT.
This idea—of doing Gimp-style manipulation on frequency-domain data and transforming back to an image—is very cool! Despite years of working with FFTs, I’ve never thought about doing this. Instead of messing with Gimp plugins and C executables and ugliness, let’s do this in Python!
Caveat. I experimented with a number of ways to do this, attempting to get something close to the output Gimp Fourier image (gray with moiré pattern) from the original input image, but I simply couldn’t. The Gimp image appears to be somewhat symmetric around the middle of the image, but it’s not flipped vertically or horizontally, nor is it transpose-symmetric. I’d expect the plugin to be using a real 2D FFT to transform an H×W image into a H×W array of real-valued data in the frequency domain, in which case there would be no symmetry (it’s just the to-complex FFT that’s conjugate-symmetric for real-valued inputs like images). So I gave up trying to reverse-engineer what the Gimp plugin is doing and looked at how I’d do this from scratch.
The code. Very simple: read an image, apply scipy.fftpack.rfft in the leading two dimensions to get the “frequency-image”, rescale to 0–255, and save.
Note how this is different from the other answers! No grayscaling—the 2D real-to-real FFT happens independently on all three channels. No abs needed: the frequency-domain image can legitimately have negative values, and if you make them positive, you can’t recover your original image. (Also a nice feature: no compromises on image size. The size of the array remains the same before and after the FFT, whether the width/height is even or odd.)
from PIL import Image
import numpy as np
import scipy.fftpack as fp
## Functions to go from image to frequency-image and back
im2freq = lambda data: fp.rfft(fp.rfft(data, axis=0),
axis=1)
freq2im = lambda f: fp.irfft(fp.irfft(f, axis=1),
axis=0)
## Read in data file and transform
data = np.array(Image.open('test.png'))
freq = im2freq(data)
back = freq2im(freq)
# Make sure the forward and backward transforms work!
assert(np.allclose(data, back))
## Helper functions to rescale a frequency-image to [0, 255] and save
remmax = lambda x: x/x.max()
remmin = lambda x: x - np.amin(x, axis=(0,1), keepdims=True)
touint8 = lambda x: (remmax(remmin(x))*(256-1e-4)).astype(int)
def arr2im(data, fname):
out = Image.new('RGB', data.shape[1::-1])
out.putdata(map(tuple, data.reshape(-1, 3)))
out.save(fname)
arr2im(touint8(freq), 'freq.png')
(Aside: FFT-lover geek note. Look at the documentation for rfft for details, but I used Scipy’s FFTPACK module because its rfft interleaves real and imaginary components of a single pixel as two adjacent real values, guaranteeing that the output for any-sized 2D image (even vs odd, width vs height) will be preserved. This is in contrast to Numpy’s numpy.fft.rfft2 which, because it returns complex data of size width/2+1 by height/2+1, forces you to deal with one extra row/column and deal with deinterleaving complex-to-real yourself. Who needs that hassle for this application.)
Results. Given input named test.png:
this snippet produces the following output (global min/max have been rescaled and quantized to 0-255):
And upscaled:
In this frequency-image, the DC (0 Hz frequency) component is in the top-left, and frequencies move higher as you go right and down.
Now, let’s see what happens when you manipulate this image in a couple of ways. Instead of this test image, let’s use a cat photo.
I made a few mask images in Gimp that I then load into Python and multiply the frequency-image with to see what effect the mask has on the image.
Here’s the code:
# Make frequency-image of cat photo
freq = im2freq(np.array(Image.open('cat.jpg')))
# Load three frequency-domain masks (DSP "filters")
bpfMask = np.array(Image.open('cat-mask-bpfcorner.png')).astype(float) / 255
hpfMask = np.array(Image.open('cat-mask-hpfcorner.png')).astype(float) / 255
lpfMask = np.array(Image.open('cat-mask-corner.png')).astype(float) / 255
# Apply each filter and save the output
arr2im(touint8(freq2im(freq * bpfMask)), 'cat-bpf.png')
arr2im(touint8(freq2im(freq * hpfMask)), 'cat-hpf.png')
arr2im(touint8(freq2im(freq * lpfMask)), 'cat-lpf.png')
Here’s a low-pass filter mask on the left, and on the right, the result—click to see the full-res image:
In the mask, black = 0.0, white = 1.0. So the lowest frequencies are kept here (white), while the high ones are blocked (black). This blurs the image by attenuating high frequencies. Low-pass filters are used all over the place, including when decimating (“downsampling”) an image (though they will be shaped much more carefully than me drawing in Gimp 😜).
Here’s a band-pass filter, where the lowest frequencies (see that bit of white in the top-left corner?) and high frequencies are kept, but the middling-frequencies are blocked. Quite bizarre!
Here’s a high-pass filter, where the top-left corner that was left white in the above mask is blacked out:
This is how edge-detection works.
Postscript. Someone, make a webapp using this technique that lets you draw masks and apply them to an image real-time!!!
There are several issues here.
1) Manual conversion to grayscale isn't good. Use Image.open("test.png").convert('L')
2) Most likely there is an issue with types. You shouldn't pass np.ndarray from fft2 to a PIL image without being sure their types are compatible. abs(np.fft.fft2(something)) will return you an array of type np.float32 or something like this, whereas PIL image is going to receive something like an array of type np.uint8.
3) Scaling suggested in the comments looks wrong. You actually need your values to fit into 0..255 range.
Here's my code that addresses these 3 points:
import numpy as np
from PIL import Image
def fft(channel):
fft = np.fft.fft2(channel)
fft *= 255.0 / fft.max() # proper scaling into 0..255 range
return np.absolute(fft)
input_image = Image.open("test.png")
channels = input_image.split() # splits an image into R, G, B channels
result_array = np.zeros_like(input_image) # make sure data types,
# sizes and numbers of channels of input and output numpy arrays are the save
if len(channels) > 1: # grayscale images have only one channel
for i, channel in enumerate(channels):
result_array[..., i] = fft(channel)
else:
result_array[...] = fft(channels[0])
result_image = Image.fromarray(result_array)
result_image.save('out.png')
I must admit I haven't managed to get results identical to the GIMP FFT plugin. As far as I see it does some post-processing. My results are all kinda very low contrast mess, and GIMP seems to overcome this by tuning contrast and scaling down non-informative channels (in your case all chanels except Red are just empty). Refer to the image:
Related
My problem is as follows. I have an image img0 (array shape (A,B,3)) and then a face img1 cut out from the middle of that image (by an algorithm I don't have access to: my input is only the whole image, and the face cut out from it), now an array shaped (C,D,3) where C<A and D<B. Now, I want to perform operations on the face (e.g., colour it differently) and then stick it back inside the original background (which is not coloured differently) -- these operations will not affect the shape of img1 array containing the face alone, it will remain (C,D,3). Something like img0-img1 doesn't work because of the shape mismatch.
I guess an approach like finding the starting coordinate of the face in img0 would work in the case that the face cut out is rectangular (which is possible for me to use, though not ideal), since it is guaranteed that the face is exactly identical in img1 and img0. That means, to get the background, we only need to find the starting coordinate of the img1 array in img0, cut out the subsequent elements (that correspond to img1) from img0, and we're left with the background. After I've done whatever I want to the face, I can use the new (C,D,3) array in place of the previous img1 part of the whole image (img0).
Is there a way to do this in Python? i.e., compute the difference between two images of different sizes, where one image is a 'subimage' of the other? Or, failing that, if we can find the starting coordinate of the rectangular portion of an image (img0) which corresponds to a rectangular cutout available to us (img1)?
Or, failing that, if we can find the starting coordinate of the rectangular ?portion of an image (img0) which corresponds to a rectangular cutout available to us (img1)?
One easy way to do that would be to cross-correlate your zero-mean cut-out with the zero-mean original image. As you have no noise added to the image, any maximum of the cross-correlation is a possible candidate.
However:
(i) If you don't use faces but e.g. blocks, there will be multiple maxima and you don't have an unique solution.
(ii) It is not exactly an elegant solution to your problem.
I modified the code example from [1] to make it clearer:
from scipy import signal, misc
import numpy as np
face = misc.face(gray=True)
face = face - np.mean(face)
face_cutout = np.copy(face[300:365, 670:750])
face_cutout = face_cutout - np.mean(face_cutout)
corr = signal.correlate2d(face, face_cutout, mode='valid')
y, x = np.unravel_index(np.argmax(corr), corr.shape) # find the match
print(f'x: {x} y: {y}')
[1] https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.correlate2d.html
I am wondering is there any workaround to convert RGB images to pixel vectors without losing its spatial information in python. As far as I know, I can read the images and do transformation for images to pixel vectors. I am not sure doing this way still preserve images' spatial information in pixel vectors. How can I make this happen for making pixel vectors from RGB image?
my attempt:
I tried as follow but I am not sure how to make
import matplotlib.pyplot as pl
image = plt.imread('dog.jpg')
im = image/255.0
print(im.shape) #(32, 32, 3)
pixels = im.reshape(im.shape[0]*im.shape[1], im.shape[2])
but I want to make sure how to make pixel vectors from RGB images without losing pixel order and its spatial information. How to make this happen? any thoughts?
I think maybe numpy might have functions to do this. Can anyone point me how to do this with numpy?
graphic illustration:
here is simple graphic illustration of making pixel vectors from RGB images:
as this diagram shows, we have RGB images with shape of (4,4,3) which needs to make pixel vectors without losing its spatial information and pixel orders then combine pixel vectors from each channel (Red, Green, Blue) as pixel matrix or dataframe. I am curious how to get this done in python?
goal:
I want to make pixel vectors from RGB images so resulted pixel vectors needs to be expanded with taylor expansion. Can anyone point me out how to make this happen?
Are You just trying to reshape each channel to a vector and then joining them horizontally? That's what I understood from the graphic illustration and the way i would do it is something like this:
import matplotlib.pyplot as plt
import numpy as np
image = plt.imread('monkey.png')
image = image / 255.0
red = image[:,:,0]
green = image[:,:,1]
blue = image[:,:,2]
def to_vector(matrix):
result = []
for i in range(matrix.shape[1]):
result = np.vstack(matrix[:,i])
return result
red = to_vector(red)
green = to_vector(green)
blue = to_vector(blue)
vector = np.hstack((red,green,blue))
Your original attempt was almost a full solution - maybe actually a full solution, depending on what the idea is.
print(im.shape) #(32, 32, 3)
pixels = im.reshape(im.shape[0]*im.shape[1], im.shape[2]) # this is exactly correct
print(pixels.shape) #(1024,3)
reds = pixels[:, 0] #just as an example for where things end up in the result
pixels_channelfirst = np.moveaxis(pixels, 1, 0) # if you want the first axis to be channels
print(pixels.shape) #(3, 1024)
reds = pixels[0, :]
"I want to preserve its pixel order and spatial information" - this does that already! Add one non-zero pixel to a zero image and plot where it goes, if you have doubts. np.hstack in the other answer does as well.
A chem student asked me for help with plotting image segmenetation:
A stationary camera takes a picture of the experimental setup every second over a period of a few minutes, so like 300 images yield.
The relevant parts in the setup are two adjacent layers of differently-colored foams observed from the side, a 2-color sandwich shrinking from both sides, basically, except one of the foams evaporates a bit faster.
I'd like to segment each of the images in the way that would let me plot both foam regions' "width" against time.
Here is a "diagram" :)
I want to go from here --> To here
Ideally, given a few hundred of such shots, in which only the widths change, I get an array of scalars back that I can plot. (Going to look like a harmonic series on either side of the x-axis)
I have a bit of python and matlab experience, but have never used OpenCV or Image Processing toolbox in matlab, or actually never dealt with any computer vision in general. Could you guys throw like a roadmap of what packages/functions to use or steps one should take and i'll take it from there?
I'm not sure how to address these things:
-selecting at which slice along the length of the slice the algorithm measures the width(i.e. if the foams are a bit uneven), although this can be ignored.
-which library to use to segment regions of the image based on their color, (some k-means shenanigans probably), and selectively store the spatial parameters of the resulting segments?
-how to iterate that above over a number of files.
Thank you kindly in advance!
Assume your Intensity will be different after converting into gray scale ( if not, just convert to other color space like HSV or LAB, then just use one of the components)
img = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)
First, Threshold your grayscaled input into a few bands
ret,thresh1 = cv.threshold(img,128,255,cv.THRESH_BINARY)
ret,thresh2 = cv.threshold(img,27,255,cv.THRESH_BINARY_INV)
ret,thresh3 = cv.threshold(img,77,255,cv.THRESH_TRUNC)
ret,thresh4 = cv.threshold(img,97,255,cv.THRESH_TOZERO)
ret,thresh5 = cv.threshold(img,227,255,cv.THRESH_TOZERO_INV)
The value should be tested out by your actual data. Here Im just give a example
Clean up the segmented image using median filter with a radius larger than 9. I do expect some noise. You can also use ROI here to help remove part of noise. But personally I`m lazy, I just wrote program to handle all cases and angle
threshholed_images_aftersmoothing = cv2.medianBlur(threshholed_images,9)
Each band will be corresponding to one color (layer). Now you should have N segmented image from one source. where N is the number of layers you wish to track
Second use opencv function bounding rect to find location and width/height of each Layer AKA each threshholed_images_aftersmoothing. Eg. boundingrect on each sub-segmented images.
C++: Rect boundingRect(InputArray points)
Python: cv2.boundingRect(points) → retval¶
Last, the rect have x,y, height and width property. You can use a simple sorting order to sort from top to bottom layer based on rect attribute x. Run though all vieo to obtain the x(layer id) , height vs time graph.
Rect API
Public Attributes
_Tp **height** // this is what you are looking for
_Tp width
_Tp **x** // this tells you the position of the band
_Tp y
By plot the corresponding heights (|AB| or |CD|) over time, you can obtain the graph you needed.
The more correct way is to use Kalman filter to track the position and height graph as I would expect some sort of bubble will occur and will interfere with the height of the layers.
To be honest, i didnt expect a chem student to be good at this. Haha good luck
Anything wrong you can find me here or Email me if i`m not watching stackoverflow
You can select a region of interest straight down the middle of the foams, a few pixels wide. If you stack these regions for each image it will show the shrink over time.
If for example you use 3 pixel width for the roi, the result of 300 images will be a 900 pixel wide image, where the left is the start of the experiment and the right is the end. The following image can help you understand:
Though I have not fully tested it, this code should work. Note that there must only be images in the folder you reference.
import cv2
import numpy as np
import os
# path to folder that holds the images
path = '.'
# dimensions of roi
x = 0
y = 0
w = 3
h = 100
# store references to all images
all_images = os.listdir(path)
# sort images
all_images.sort()
# create empty result array
result = np.empty([h,0,3],dtype=np.uint8)
for image in all_images:
# load image
img = cv2.imread(path+'/'+image)
# get the region of interest
roi = img[y:y+h,x:x+w]
# add the roi to previous results
result = np.hstack((result,roi))
# optinal: save result as image
# cv2.imwrite('result.png',result)
# display result - can also plot with matplotlib
cv2.imshow('Result', result)
cv2.waitKey(0)
cv2.destroyAllWindows()
Update after question edit:
If the foams have different colors, your can use easily separate them by color by converting the image you hsv and using inrange (example). This creates a mask (=2D array with values from 0-255, one for each pixel) that you can use to calculate average height and extract the parameters and area of the image.
You can find a script to help you find the HSV colors for separation on this GitHub
I am trying to convert an image into an array of pixels.
Here is my current code.
im = Image.open("beeleg.png")
pixels = im.load()
im.getdata() # doesn't work
print(pixels # doesn't work
Ideally, my end goal is to convert the image into a vector of just pixels, so for instance if I have an image of dimensions 100x100, then I want a vector of dimensions 1x10000, where each value is between [0, 255]. Then, divide each of the values in the array by 256 and add a bias of 1 in the front of the vector. However, I am not able to proceed with all this without being able to obtain an array. How to proceed?
Scipy's ndimage library is generally the go-to library for working with pixels as data (arrays). You can load an image from file (most common formats supported) using scipy.ndimage.imread into a numpy array which can be easily reshaped and mathematically operated on. The mode keyword can be used to specify a colorspace transformation upon load (convert an RGB image to black and white). In your case you asked for single color pixels from 0-255 (8bit grayscale) so you would use mode='L'. See The Documentation for usage / more useful functions.
If use OpenCV, gray=cv2.imread(image,0) will return a grayscale image with n rows x m cols single channel numpy array. rows, cols = gray.shape will return the height and width of the image.
Is there any good algorithm for detecting particles on a changing background intensity?
For example, if I have the following image:
Is there a way to count the small white particles, even with the clearly different background that appears towards the lower left?
To be a little more clear, I would like to label the image and count the particles with an algorithm that finds these particles to be significant:
I have tried many things with the PIL, cv , scipy , numpy , etc. modules.
I got some hints from this very similar SO question, and it appears at first glance that you could take a simple threshold like so:
im = mahotas.imread('particles.jpg')
T = mahotas.thresholding.otsu(im)
labeled, nr_objects = ndimage.label(im>T)
print nr_objects
pylab.imshow(labeled)
but because of the changing background you get this:
I have also tried other ideas, such as a technique I found for measuring paws, which I implemented in this way:
import numpy as np
import scipy
import pylab
import pymorph
import mahotas
from scipy import ndimage
import cv
def detect_peaks(image):
"""
Takes an image and detect the peaks usingthe local maximum filter.
Returns a boolean mask of the peaks (i.e. 1 when
the pixel's value is the neighborhood maximum, 0 otherwise)
"""
# define an 8-connected neighborhood
neighborhood = ndimage.morphology.generate_binary_structure(2,2)
#apply the local maximum filter; all pixel of maximal value
#in their neighborhood are set to 1
local_max = ndimage.filters.maximum_filter(image, footprint=neighborhood)==image
#local_max is a mask that contains the peaks we are
#looking for, but also the background.
#In order to isolate the peaks we must remove the background from the mask.
#we create the mask of the background
background = (image==0)
#a little technicality: we must erode the background in order to
#successfully subtract it form local_max, otherwise a line will
#appear along the background border (artifact of the local maximum filter)
eroded_background = ndimage.morphology.binary_erosion(background, structure=neighborhood, border_value=1)
#we obtain the final mask, containing only peaks,
#by removing the background from the local_max mask
detected_peaks = local_max - eroded_background
return detected_peaks
im = mahotas.imread('particles.jpg')
imf = ndimage.gaussian_filter(im, 3)
#rmax = pymorph.regmax(imf)
detected_peaks = detect_peaks(imf)
pylab.imshow(pymorph.overlay(im, detected_peaks))
pylab.show()
but this gives no luck either, showing this result:
Using the regional max function, I get images which almost appear to be giving correct particle identification, but there are either too many, or too few particles in the wrong spots depending on my gaussian filtering (images have gaussian filter of 2,3, & 4):
Also, it would need to work on images similar to this as well:
This is the same type of image above, just at a much higher density of particles.
EDIT: Solved solution: I was able to get a decent working solution to this problem using the following code:
import cv2
import pylab
from scipy import ndimage
im = cv2.imread('particles.jpg')
pylab.figure(0)
pylab.imshow(im)
gray = cv2.cvtColor(im, cv2.COLOR_BGR2GRAY)
gray = cv2.GaussianBlur(gray, (5,5), 0)
maxValue = 255
adaptiveMethod = cv2.ADAPTIVE_THRESH_GAUSSIAN_C#cv2.ADAPTIVE_THRESH_MEAN_C #cv2.ADAPTIVE_THRESH_GAUSSIAN_C
thresholdType = cv2.THRESH_BINARY#cv2.THRESH_BINARY #cv2.THRESH_BINARY_INV
blockSize = 5 #odd number like 3,5,7,9,11
C = -3 # constant to be subtracted
im_thresholded = cv2.adaptiveThreshold(gray, maxValue, adaptiveMethod, thresholdType, blockSize, C)
labelarray, particle_count = ndimage.measurements.label(im_thresholded)
print particle_count
pylab.figure(1)
pylab.imshow(im_thresholded)
pylab.show()
This will show the images like this:
(which is the given image)
and
(which is the counted particles)
and calculate the particle count as 60.
I had solved the "variable brightness in background" by using a tuned difference threshold with a technique called Adaptive Contrast. It works by performing a linear combination (a difference, in the case) of a grayscale image with a blurred version of itself, then applying a threshold to it.
Convolve the image with a suitable statistical operator.
Subtract the original from the convolved image, correcting intensity scale/gamma if necessary.
Threshold the difference image with a constant.
(original paper)
I did this very successfully with scipy.ndimage, in the floating-point domain (way better results than integer image processing), like this:
original_grayscale = numpy.asarray(some_PIL_image.convert('L'), dtype=float)
blurred_grayscale = scipy.ndimage.filters.gaussian_filter(original_grayscale, blur_parameter)
difference_image = original_grayscale - (multiplier * blurred_grayscale);
image_to_be_labeled = ((difference_image > threshold) * 255).astype('uint8') # not sure if it is necessary
labelarray, particle_count = scipy.ndimage.measurements.label(image_to_be_labeled)
Hope this helps!!
I cannot really give a definite answer, but here are a few pointers:
The function mahotas.morph.regmax might be better than the maximum filter as it removes pseudo-maxima. Perhaps combine this with a global threshold, with a local threshold (such as the mean over a window) or both.
If you have several images and the same uneven background, then maybe you can compute an average background and normalize against that, or use empty images as your estimate of background. This would be the case if you have a microscope, and like every microscope I've seen, the illumination is uneven.
Something like:
average = average_of_many(images)
# smooth it
average = mahotas.gaussian_filter(average,24)
Now you preprocess your images, like:
preproc = image/average
or something like that.