simple case of optical flow

General: I'm hoping that the use-case I'm about to describe is a simple case of an optical flow problem and since I don't have much knowledge on the subject, I was wondering if anyone has any suggestions on how I can approach solving my problem.

Research I've already done: I have began reading the High Accuracy Optical Flow Estimation Based on a Theory for Warping paper and am planning on looking over the Particle Video paper. I have found a MATLAB High Accuracy Optical Flow implementation of optical flow. However, the papers (and the code) seem to describe concepts that are very involved and may require a lot of time for me to dig in and understand. I am hoping that the solution to my problem may be more simple.

Problem: I have a sequence of images. The images depict a material breakage process, where the material and background are black and the cracks are white. I am interested in traversing the sequence of images in reverse in an attempt to map all of the cracks that have formed in the breakage process to the first black image. You can think of the material as a large puzzle and I am trying to put the pieces back together in the reverse order that they broke.

In each image, there can be some cracks that are just emerging and/or some cracks that have been fully formed (and thus created a fragment). Throughout the breakage process, some fragments may separate and break further. The fragments can also move farther away from one another (the change is slight between subsequent frames).

Desired Output: All of the cracks/lines in the开发者_如何学Go sequence mapped to the first image in the sequence.

Additional Notes: Images are available in grayscale format (i.e. original) as well as in binary format, where the cracks have been outlined in white and the background is completely black. See below for some image examples.

The top row shows the original images and the bottom row shows the binary images. As you can see, the crack that goes down the middle grows wider and wider as the image sequence progresses. Thus, the bottom crack moves together with the lower fragment. When traversing the sequence in reverse, I hope to algorithmically realize that the middle crack comes together as one (and map it correctly to the first image), and also map the bottom crack correctly, keeping its correct correspondence (size and position) with the bottom fragment.

A sequence typically contains about 30~40 images, so I've just shown the beginning subset. Also, although these images don't show it, it is possible that a particular image only contains the beginning of the crack (i.e. its initial appearance) and in subsequent images it gets longer and longer and may join with other cracks.

Language: Although not necessary, I would like to implement the solution using MATLAB (just because most of the other code that relates to the project has been done in MATLAB). However, if OpenCV may be easier, I am flexible in my language/library usage.

Any ideas are greatly appreciated.

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Traverse forward rather than reverse, and don't use optical flow. Use the fracture lines to segment the black parts, track the centroid of each black segment over time. Whenever a new fracture line appears that cuts across a black segment, split the segment into two and continue tracking each segment separately.

From this you should be able to construct a tree structure representing the segmentation of the black parts over time. The fracture lines can be added as metadata to this tree, perhaps assigning fracture lines to the segment node in which they first appeared.

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I would advise you to follow your initial idea of backtracking the cracks. Yo kind of know how the cracks look like so you can track all the points that belong to the crack. You just track all the white points with an optical flow tracker, start with Lukas-Kanade tracker and see where you get. The high-accuracy optical flow method is a global one and more general, I'll track all the pixels in the image trying to keep some smoothness everywhere. The LK is a local method that will just use a small window around each point to do the tracking. The problem is that appart from the cracks all the pixels are plain black so nothing to track there, you'll just waist time trying to track something that you can't track and you don't need to track. If lines are very straight you might end up with what's called the aperture problem and you'll get inaccurate results. You can also try some shape fitting/deformation based on snakes.

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I agree to damian. Most optical flow methods like the HAOF rely on the first-order taylor approximation of the intensity constancy constrian equation I(x,t)=I(x+v,t+dt). That mean the solution depends on image derivatives where the gradient determine the motion vector magnitude and angle i.e. you need a certain amount of texture. However the very low texture of your non-binarised images could be enough. You could try histogram equalization to increase the contrast of your input data but it is important to apply the same transformation for both input images. e.g. as follows:

cv::Mat equalizeMat(grayInp1.rows, grayInp1.cols * 2 , CV_8UC1);
grayInp1.copyTo(equalizeMat(cv::Rect(0,0,grayInp1.cols,grayInp1.rows))); 
grayInp2.copyTo(equalizeMat(cv::Rect(grayInp1.cols,0,grayInp2.cols,grayInp2.rows)));
cv::equalizeHist(equalizeMat,equalizeMat);
equalizeMat(cv::Rect(0,0,grayInp1.cols,grayInp1.rows)).copyTo(grayInp1);
equalizeMat(cv::Rect(grayInp1.cols,0,grayInp2.cols,grayInp2.rows)).copyTo(grayInp2);
// estimate optical flow