Robust tracking of blobs - python

I have an image feature extraction problem. The input images are binary (black and white) and may contain blobs of approximately known area and aspect ratio. These need to be fit with ellipses using some best fit algorithm.
Example input:
Desired output:
There may be multiple blobs (zero or more), the number is not known in advance. The approximate area and aspect ratio of all the blobs is known (and is the same). How many are in the image, their position, orientation and actual size are what I'm trying to find. The output should be a best fit ellipse for each blob based on the actual found size and aspect ratio.
What makes this hard is noise and possible overlaps.
Example with noise:
Example with overlap and noise:
The noisy image may have holes in the blobs and also small other blobs scattered around. The small other blobs are not counted because they are too small and do not cover any area densely enough to be considered a real match.
The image with overlap should be counted as two blobs because the area is too big for a single blob to cover it well.
A possible metric that evaluates a potential fit is:
sum over all ellipses of (K1 * percent deviation from expected size + K2 * percent deviation from expected aspect ratio + K3 * percent of ellipse which is not black + K4 * percent overlapped with any other ellipse) + K5 * percent of rest of image which is black
for some suitably chosen parameters K1..K5. A perfect match scores 0.
I can see how to solve this using brute force, for example trying enough different possible fits to sample the search space well. I can't think off-hand of a method much faster than brute force.
I would prefer examples in python and/or opencv. I will try to implement and post any suggested solutions in python. Thanks!
P.S. It cannot be assumed that a blob is connected. There may be enough noise to break it up into discontinuous parts.
P.P.S. The little bits of noise cannot be removed by binary erosion. In some of my images, there are enough interior holes that erosion makes the whole (real) blob disappear if the image is eroded enough to make the noise bits disappear as well.
P.P.P.S. I think that it would be very hard to solve this using any approach based on contours. The data I see in practice has too much edge noise, there can be (and often are) bits of noise that connect separate blobs, or that separate a single blob into several (apparent) connected components. I would like an approach based on areas, since area coverage seems to be much less nosy than the edge shapes.
P.P.P.P.S. As requested, here is an example with a through cut due to noise:
and a sample with lots and lots of noise but nevertheless a distinct blob:
EDIT None of the answers actually solves the problem, although Bharat has suggested a partial solution which does well for non-overlapping blobs. More please :) I will award additional bounty to any actual solutions.

I would try to fit a gaussian mixture model and then use the mean and the covariance matrix to fit ellipses over the data. Such a model would work even with overlap and small noisy blobs. The data which you have would be the the coordinates of the pixels which are black and you could fit a GMM over the data. One issue with this approach is that you need to know the number of blobs you need to track in advance, if you can come up with a heuristic for that, GMM should solve this problem pretty efficiently.

You fill the holes [1], you detect contours [2], and use moments on each contour rectangle to find orientation, eccentricity, etc[3].
PS.: The disconnected contours (noise) can be filtered out by size.

You might start by filtering out contours by area.
About separating overlapping blobs, that might be a tricky one (I would risk to say, impossible for arbitrary overlaps) to do with this binary image, maybe you should do it with the original image or at least some steps back of pre-processing.
OpenCV's fittEllipse will also be helpful.

this is not some basic programming problem, this involves advanced image processing techniques. from what I know, "Image Processing, morphology" are the points you are targeting for. you can take some course in "Image Morphology" understand those basic constructs such as "Dilation, Erosion" etc... then you have the fundamentals solving this issue at hand.

Since you have the size and orientation, you can draw each ellipse, and use template matching.
see tutorial here.

Related

Skewing text - How to take advantage of existing edges

I have the following JPG image. If I want to find the edges where the white page meets the black background. So I can rotate the contents a few degrees clockwise. My aim is to straighten the text for using with Tesseract OCR conversion. I don't see the need to rotate the text blocks as I have seen in similar examples.
In the docs Canny Edge Detection the third arg 200 eg edges = cv.Canny(img,100,200) is maxVal and said to be 'sure to be edges'. Is there anyway to determine these (max/min) values ahead of any trial & error approach?
I have used code examples which utilize the Python cv2 module. But the edge detection is set up for simpler applications.
Is there any approach I can use to take the text out of the equation. For example: only detecting edge lines greater than a specified length?
Any suggestions would be appreciated.
Below is an example of edge detection (above image same min/max values) The outer edge of the page is clearly defined. The image is high contrast b/w. It has even lighting. I can't see a need for the use of an adaptive threshold. Simple global is working. Its just at what ratio to use it.
I don't have the answer to this yet. But to add. I now have the contours of the above doc.
I used find contours tutorial with some customization of the file loading. Note: removing words gives a thinner/cleaner outline.
Consider Otsu.
Its chief virtue is that it is adaptive to local
illumination within the image.
In your case, blank margins might be the saving grace.
Consider working on a series of 2x reduced resolution images,
where new pixel is min() (or even max()!) of original four pixels.
These reduced images might help you to focus on the features
that matter for your use case.
The usual way to deskew scanned text is to binarize and
then keep changing theta until "sum of pixels across raster"
is zero, or small. In particular, with few descenders
and decent inter-line spacing, we will see "lots" of pixels
on each line of text and "near zero" between text lines,
when theta matches the original printing orientation.
Which lets us recover (1.) pixels per line, and (2.) inter-line spacing, assuming we've found a near-optimal theta.
In your particular case, focusing on the ... leader dots
seems a promising approach to finding the globally optimal
deskew correction angle. Discarding large rectangles of
pixels in the left and right regions of the image could
actually reduce noise and enhance the accuracy of
such an approach.

Identifying positive pixels after color deconvolution ignoring boundaries

I am analyzing histology tissue images stained with a specific protein marker which I would like to identify the positive pixels for that marker. My problem is that thresholding on the image gives too much false positives which I'd like to exclude.
I am using color deconvolution (separate_stains from skimage.color) to get the AEC channel (corresponding to the red marker), separating it from the background (Hematoxylin blue color) and applying cv2 Otsu thresholding to identify the positive pixels using cv2.threshold(blur,0,255,cv2.THRESH_BINARY+cv2.THRESH_OTSU), but it is also picking up the tissue boundaries (see white lines in the example picture, sometimes it even has random colors other than white) and sometimes even non positive cells (blue regions in the example picture). It's also missing some faint positive pixels which I'd like to capture.
Overall: (1) how do I filter the false positive tissue boundaries and blue pixels? and (2) how do I adjust the Otsu thresholding to capture the faint red positives?
Adding a revised example image -
top left the original image after using HistoQC to identify tissue regions and apply the mask it identified on the tissue such that all of the non-tissue regions are black. I should tru to adjust its parameters to exclude the folded tissue regions which appear more dark (towards the bottom left of this image). Suggestions for other tools to identify tissue regions are welcome.
top right hematoxylin after the deconvolution
bottom left AEC after the deconvolution
bottom right Otsu thresholding applied not the original RGB image trying to capture only the AEC positives pixels but showing also false positives and false negatives
Thanks
#cris-luengo thank you for your input on scikit-image! I am one of the core developers, and based on #assafb input, we are trying to rewrite the code on color/colorconv/separate_stains.
#Assafb: The negative log10 transformation is the Beer-Lambert mapping. What I don't understand in that code is the line rgb += 2. I don't know where that comes from or why they use it. I'm 100% sure it is wrong. I guess they're trying to avoid log10(0), but that should be done differently. I bet this is where your negative values come from, though.
Yes, apparently (I am not the original author of this code) we use rgb += 2 to avoid log10(0). I checked Fiji's Colour Deconvolution plugin, and they add 1 to their input. I tested several input numbers to help on that, and ~2 would let us closer to the desirable results.
#Assafb: Compare the implementation in skimage with what is described in the original paper. You'll see several errors in the implementation, most importantly the lack of a division by the max intensity. They should have used -np.log10(rgb/255) (assuming that 255 is the illumination intensity), rater than -np.log10(rgb).
Our input data is float; the max intensity in this case would be 1. I'd say that that's the reason we don't divide by something.
Besides that, I opened an issue on scikit-image to discuss these problems — and to specify a solution. I made some research already — I even checked DIPlib's documentation —, and implemented a different version of that specific function. However, stains are not my main area of expertise, and we would be glad if you could help evaluating that code — and maybe pointing a better solution.
Thank you again for your help!
There are several issues that cause improper quantification. I'll go over the details of how I would recommend you tackle these slides.
I'm using DIPlib, because I'm most familiar with it (I'm an author). It has Python bindings, which I use here, and can be installed with pip install diplib. However, none of this is complicated image processing, and you should be able to do similar processing with other libraries.
Loading image
There is nothing special here, except that the image has strong JPEG compression artifacts, which can interfere with the stain unmixing. We help the process a bit by smoothing the image with a small Gaussian filter.
import diplib as dip
import numpy as np
image = dip.ImageRead('example.png')
image = dip.Gauss(image, [1]) # because of the severe JPEG compression artifacts
Stain unmixing
[Personal note: I find it unfortunate that Ruifrok and Johnston, the authors of the paper presenting the stain unmixing method, called it "deconvolution", since that term already had an established meaning in image processing, especially in combination with microscopy. I always refer to this as "stain unmixing", never "deconvolution".]
This should always be the first step in any attempt at quantifying from a bightfield image. There are three important RGB triplets that you need to determine here: the RGB value of the background (which is the brightness of the light source), and the RGB value of each of the stains. The unmixing process has two components:
First we apply the Beer-Lambert mapping. This mapping is non-linear. It converts the transmitted light (as recorded by the microscope) into absorbance values. Absorbance indicates how strongly each point on the slide absorbs light of the various wavelengths. The stains absorb light, and differ by the relative absorbance in each of the R, G and B channels of the camera.
background_intensity = [209, 208, 215]
image = dip.BeerLambertMapping(image, background_intensity)
I manually determined the background intensity, but you can automate that process quite well if you have whole slide images: in whole slide images, the edges of the image always correspond to background, so you can look there for intensities.
The second step is the actual unmixing. The mixing of absorbances is a linear process, so the unmixing is solving of a set of linear equations at each pixel. For this we need to know the absorbance values for each of the stains in each of the channels. Using standard values (as in skimage.color.hax_from_rgb) might give a good first approximation, but rarely will provide the best quantification.
Stain colors change from assay to assay (for example, hematoxylin has a different color depending on who made it, what tissue is stained, etc.), and change also depending on the camera used to image the slide (each model has different RGB filters). The best way to determine these colors is to prepare a slide for each stain, using all the same protocol but not putting on the other dyes. From these slides you can easily obtain stain colors that are valid for your assay and your slide scanner. This is however rarely if ever done in practice.
A more practical solution involves estimating colors from the slide itself. By finding a spot on the slide where you see each of the stains individually (where stains are not mixed) one can manually determine fairly good values. It is possible to automatically determine appropriate values, but is much more complex and it'll be hard finding an existing implementation. There are a few papers out there that show how to do this with non-negative matrix factorization with a sparsity constraint, which IMO is the best approach we have.
hematoxylin_color = np.array([0.2712, 0.2448, 0.1674])
hematoxylin_color = (hematoxylin_color/np.linalg.norm(hematoxylin_color)).tolist()
aec_color = np.array([0.2129, 0.2806, 0.4348])
aec_color = (aec_color/np.linalg.norm(aec_color)).tolist()
stains = dip.UnmixStains(image, [hematoxylin_color, aec_color])
stains = dip.ClipLow(stains, 0) # set negative values to 0
hematoxylin = stains.TensorElement(0)
aec = stains.TensorElement(1)
Note how the linear unmixing can lead to negative values. This is a result of incorrect color vectors, noise, JPEG artifacts, and things on the slide that absorb light that are not the two stains we defined.
Identifying tissue area
You already have a good method for this, which is applied to the original RGB image. However, don't apply the mask to the original image before doing the unmixing above, keep the mask as a separate image. I wrote the next bit of code that finds tissue area based on the hematoxylin stain. It's not very good, and it's not hard to improve it, but I didn't want to waste too much time here.
tissue = dip.MedianFilter(hematoxylin, dip.Kernel(5))
tissue = dip.Dilation(tissue, [20])
tissue = dip.Closing(tissue, [50])
area = tissue > 0.2
Identifying tissue folds
You were asking about this step too. Tissue folds typically appear as larger darker regions in the image. It is not trivial to find an automatic method to identify them, because a lot of other things can create darker regions in the image too. Manual annotation is a good start, if you collect enough manually annotated examples you could train a Deep Learning model to help you out. I did this just as a place holder, again it's not very good, and identifies some positive regions as folds. Folds are subtracted from the tissue area mask.
folds = dip.Gauss(hematoxylin - aec, [20])
area -= folds > 0.2
Identifying positive pixels
It is important to use a fixed threshold for this. Only a pathologist can tell you what the threshold should be, they are the gold-standard for what constitutes positive and negative.
Note that the slides must all have been prepared following the same protocol. In clinical settings this is relatively easy because the assays used are standardized and validated, and produce a known, limited variation in staining. In an experimental setting, where assays are less strictly controlled, you might see more variation in staining quality. You will even see variation in staining color, unfortunately. You can use automated thresholding methods to at least get some data out, but there will be biases that you cannot control. I don't think there is a way out: inconsistent stain in, inconsistent data out.
Using an image-content-based method such as Otsu causes the threshold to vary from sample to sample. For example, in samples with few positive pixels the threshold will be lower than other samples, yielding a relative overestimation of the percent positive.
positive = aec > 0.1 # pick a threshold according to pathologist's idea what is positive and what is not
pp = 100 * dip.Count(dip.And(positive, area)) / dip.Count(area)
print("Percent positive:", pp)
I get a 1.35% in this sample. Note that the % positive pixels is not necessarily related to the % positive cells, and should not be used as a substitute.
I ended up incorporating some of the feedback given above by Chris into the following possible unconventional solution for which I would appreciate getting feedback (to the specific questions below but also general suggestions for improvement or more effective/accurate tools or strategy):
Define (but not apply yet) tissue mask (HistoQC) after optimizing HistoQC script to remove as much of the tissue folds as possible without removing normal tissue area
Apply deconvolution on the original RGB image using hax_from_rgb
Using the second channel which should correspond to the red stain pixels, and subtract from it the third channel which as far as I see corresponds to the background non-red/blue pixels of the image. This step removes the high values in the second channel that which up because of tissue folds or other artifacts that weren't removed in the first step (what does the third channel correspond to? The Green element of RGB?)
Blur the adjusted image and threshold based on the median of the image plus 20 (Semi-arbitrary but it works. Are there better alternatives? Otsu doesn't work here at all)
Apply the tissue regions mask on the thresholded image yielding only positive red/red-ish pixels without the non-tissue areas
Count the % of positive pixels relative to the tissue mask area
I have been trying to apply, as suggested above, the tissue mask on the deconvolution red channel output and then use Otsu thresholding. But it failed since the black background generated by the applying the tissue regions mask makes the Otsu threshold detect the entire tissue as positive. So I have proceeded instead to apply the threshold on the adjusted red channel and then apply the tissue mask before counting positive pixels. I am interested in learning what am I doing wrong here.
Other than that, the LoG transformation didn't seem to work well because it produced a lot of stretched bright segments rather than just circular blobs where cells are located. I'm not sure why this is happening.
Use ML for this case.
Create manually binary mask for your pictures: each red pixel - white, background pixels - black.
Work in HSV or Lab color space.
Train simple classifier: decision tree or SVM (linear or with RBF)..
Let's test!
See on a good and very simple example with skin color segmentation.
And in the future you can add new examples and new cases without code refactoring: just update dataset and retrain model.

OpenCV - How to remove convexity defects in a cam scanner?

I get in trouble by finding an algorithm to remove the convexity of my photos. As you can see the photos are captured from book pages, and I wanna remove the convexity. My question is similar to this but what I have is just page boundaries as input and neither I have grid nor am able to find by processing algorithms.
I wanna output as the right one in the below photo.
Obviously, the perspective transformation is the first thing comes in mind. However, as you can see the result is not promising:
Here's a possible pipeline to solve your problem. The main idea is to identify the text, create a super blob of it with some morphology, locate the 4 corners of this super blob and feed the points to a perspective "unwarper" (or rectifier, or whatever you wish to call that perspective correction method).
Start by converting your image to grayscale and apply adaptive thresholding to it. Try the Gaussian or Mean methods with parameters that better fit your tests. This is the result I obtain after fiddling with the values for a bit:
Now, the idea is to isolate just the text. The solution I applied is: obtain the biggest blobs and subtract them from the original image. You're going to need a method to calculate the area of each binary blob. Check this previous post for suggestions on how to implement one.
These are the biggest blobs from the image:
Subtract the largest blobs from the original image. This is the result:
As you can see, the text is almost isolated. Let me clean up the little bits of pixels by applying, again, an area filter. This time to eliminate the small blobs. This is the result:
Very good, some characters are lost during the operation, but that’s ok. We need a nice continuous block of text, because we are gonna dilate the hell of it. I tried applying a rectangular structuring element of size 5 and 5 Op iterations. Erode the output with 5 more iterations afterward, so you end up with this nice - isolated - super blob were the text used to be:
Check it out. The 3 markers you see are the centroids of the biggest blobs that I detected on the image. We need to find the 4 corners of the super blob. The biggest blob in the image is what we are after. I decided to re-use the area filter and look for the blob with the biggest area. This is the isolated super blob:
From here, the operations are pretty straightforward. Again, the goal is to get the four corners of this blob. You can fit a rectangle or apply an edge detector followed by Hough transform, to get the straight lines that follow the edges of the super blob.
I decided to apply a Canny Edge detector followed by Hough transform. Of course, I tuned the transform to filter only the possible lines I’m interested in – straight lines above a certain length. This is the result of the line detection:
There's some extra info plotted on the image. The markers you see (red and yellow) are the start/endpoints of the lines. My idea here was to find a bunch of these lines and compute the mean of these points. The idea is that we have a cluster of points that are separated in "quadrants". If we compute the mean of the start and endpoints of each line per quadrant, we will end up with 4 means – and these are the approximate values of the super blob’s corners!
I applied K-means to the start and endpoints of the lines, but you very well prefer other methods of processing. That's ok. My approximate corners are identified by the big red O markers in the above image.
As I suggested, try giving a fixed output position for these corners. I defined the red rectangle for the corners to be mapped on. For this test, I pretty much adjusted the rectangle manually. The perspective correction yields this result:
Some suggestions:
Depending on the resolution of the input image, you could downsize it
for a faster and better result, as your input seems big enough for
that.
Tune Hough Line Detection to yield larger lines. My current
configuration detects some smaller lines and that can hinder the
corner approximation.
I choose a somewhat robust method for calculating the 4 corners of
the super blob that I’ve personally used before (Edge detection +
Hough Line Transform + K-means) but whatever processing chain you
chose to obtain the data is entirely up to you!

Erosion without losing regions

I have an image containing cells. I can't provide it, but it is similar to the image used as an example here: http://blogs.mathworks.com/steve/2006/06/02/cell-segmentation/ but without the characteristic nuclei.
I have done some processing and am now left with a pretty good segmentation, but some cells are close to each other and I need to split them. Most of them consist of more or less overlapping ellipses.
I am certain that a few iterations of simple erosion will split almost all of those regions. But some of the other cells are so small, they will disappear before the others split. Therefore I need an algorithm that erodes the image, allowing region splitting, but does not delete the last pixel of a region.
I want to use watershed afterwards to segment the cells.
I guess I could implement this on my own by searching for cennected regions and then tracking that I don't lose any or something like that, but the implementation seems messy even in my head and I think there must be an easier way. So my question is basically, what's the name of this so I can google an implementation? Or if there is no off-the-shelf solution, what's an elegant way of implementing this without dozens of iterations and for loops etc.
(Language is python)
It's a classical problem, and if the overlap between cells is too important, let's say 40% or more, then there is not a good solution.
However, if the overlap is not important, here is the solution:
You start from the segmentation you have, let's call it S
You computer the ultimate eroded UE(S). It will give you the center of each cell. It will give you something like the red points on this image. In this image, they use a distance map, an ultimate eroded will be more stable. If there are still many red points per cell, then a dilation of the UE(S) will fix your problem like this example.
You invert Inv(S) or compute the voronoi diagram Voi(S) in order to have a marker in the background.
Watershed on the gradient image of S, using the UE(S) as inner marker (perfect because you have one point by cell) and Inv(S) or Voi(S) as background/outer marker.
You will get something like this example.

calculate particle size distribution from AFM measurements

I am trying to obtain a radius and diameter distribution from some AFM (Atomic force microscopy) measurements. So far I am trying out Gwyddion, ImageJ and different workflows in Matlab.
At the moment the best results I have found is to use Gwyddion and to take the Phase image, high pass filter it and then try an edge detection with 'Laplacian of Gaussian'. The result is shown in figure 3. However this image is still too noisy and doesnt really capture the edges of all the particles. (some are merged together others do not have a clear perimeter).
In the end I need an image which segments each of the spherical particles which I can use for blob detection/analysis to obtain size/radius information.
Can anyone recommend a different method?
[
I would definitely try a Granulometry, it was designed for something really similar. There is a good explanation of granulometry here starting page 158.
The granulometry will perform consecutive / increasing openings that will erase the different patterns according to their dimensions. The bigger the pattern, the latter it will be erased. It will give you a curve that represent the pattern dimension distributions in your image, so exactly what you want.
However, it will not give you any information about the position inside the image. If you want to have a rough modeling of the blobs present in your image, you can take a look to the Ultimate Opening.
Maybe you can use Avizo, it's a powerful software for dealing with image issues, especially for three D data (CT)

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