I have implemented an opensource PCA code in my fortran code,
I just input the multidimentional data in to a 2 DIM matrix ( PCA_MATRIX(imagepixels_amount,image_count))
and out come the first (up to) 7 transformed images of the PCA (they are written into the input matrix)
it works fine in most cases, but in some i get an inverse pattern (in the first 3 components) which I do not understand, because all input images show a similar pattern.
Am i missing a fundamental property of PCA which can cause such inverted patterns?
the library I'm using is: http://ftp.uni-bayreuth.de/math/statlib/multi/pca
I'm thankfull for any input, i wasnt able to find anything on pca inversion online
this is an example image:
it was due to an error in the algorithm when calculating the new components from the eigenvectors, they were added/multiplied in the wrong order
Related
I have calculated the essential matrix using the 5 point algorithm. I'm not sure how to integrate it with ransac so it gives me a better outcome.
Here is the source code. https://github.com/lunzhang/openar/blob/master/src/utils/5point/computeEssential.js
Currently, I was thinking about computing the essential matrix for 5 random points then convert the essential matrix to fundamental and see the error threshold using this equation x'Fx = 0. But then I'm not sure, what to do after.
How do I know which points to set as outliners? If the errors too big, do I set them as outliners right away? Could it be possible that one point could produce different essential matrices depending on what the other 4 points are?
Well, here is a short explanation, in pseudo-code, of how you can integrate this with ransac. Basically, all Ransac does is compute your model (here the Essential) using a subset of the data, and then sees if the rest of data "is happy" with that result. It keeps the result for which a highest portion of the dataset "is happy".
highest_number_of_happy_points=-1;
best_estimated_essential_matrix=Identity;
for iter=1 to max_iter_number:
n_pts=get_n_random_pts(P);//get a subset of n points from the set of points P. You can use 5, but you can also use more.
E=compute_essential(n_pts);
number_of_happy_points=0;
for pt in P:
//we want to know if pt is happy with the computed E
err=cost_function(pt,E);//for example x^TFx as you propose, or X^TEX with the essential.
if(err<some_threshold):
number_of_happy_points+=1;
if(number_of_happy_points>highest_number_of_happy_points):
highest_number_of_happy_points=number_of_happy_points;
best_estimated_essential_matrix=E;
This should do the trick. Usually, you set some_threshold experimentally to a low value. There are of course more sophisticated Ransacs, you can easily find them by googling.
Your idea of using x^TFx is fine in my opinion.
Once this Ransac completes, you will have best_estimated_essential_matrix. The outliers are those that have a x^TFx value that is greater than your optional threshold.
To answer your final question, yes, a point could produce a different matrix given 4 different points, because their spatial configuration is different (you can have degenerate situations). In an ideal settings this wouldn't be the case, but we always have noise, matching errors and so on, so what happens in the end is that the equations you obtain with 5 points wont produce the exact same results as for 5 other points.
Hope this helps.
I'm currently working on a project where I have to compare similar histograms of image intensity. These histograms are obtained from photos taken under different illumination conditions.
I know that OpenCV offers the compareHist function. However this function returns a metric of similarity and I'm looking for a method that matches corresponding peaks/valleys between similar histograms.
For instance, if we have two photos of the same subject, one underexposed and one with the "ideal" exposure, their histograms of intensity might look something like the image in the following URL:
http://i.stack.imgur.com/tLIGR.png
As shown by the arrows, the peaks in one histogram also exist in the other. Anyone has a suggestion on how to match corresponding peaks?
Thank you!
You can use an implementation of DTW (https://en.wikipedia.org/wiki/Dynamic_time_warping) to compare the histograms.
Using dynamic programming, you can create a matrix that calculates DTW. Then, you can trace back through the matrix to find the relations between different parts of the histograms.
After that, it's simply a matter of extracting only the peaks.
I need to implement a very simple filter that suppresses a range of frequencies.
Then I need to compute the inverse Fourier transform and save the new image.
I am using the CImg library ( C++ ).
So far I have done:
const CImg<unsigned char> img(source_img);
CImgList<> F = img.get_FFT();
and I am stuck here.
F is a a list of two CImg objects the real and Imaginary part , correct?
Having this F how I suppress frequencies and reconstruct the new Image?
P.S. This is a homework, so I don't want a solution but an explanation of what to do,
how to do it and why.
Since it's homework, do feel free to experiment.
The first step you need to get working is to directly transform the image back, and get the original input. If this doesn't work, you'd be quite happy to catch it early.
The second step is to just zero some part of the FFT, transform the result back, and see how it differs. Each pixel in the FFT represents a frequency in the input, so experiment to find the relation. Then explain that relation to yourself.
Finally, once you have figured out which are of pixels you want to zero and which ones to keep, create a black& white mask, turn that into a greyscale image, and then blur it. A sharp edge in the FFT domain has an infinite support in the image domain - in practice, that causes additional fake edges. It's better to have a single blurred edge.
I am trying to use two Gaussian mixtures with EM algorithm to estimate color distribution of a video frame. For that, I want to use two separate peaks in the color distribution as the two Gaussian means to facilitate the EM calculation. I have several difficulties with the implementation of these in OpenCV.
My first question is: how can I determine the two peaks? I've searched about peak estimation in OpenCV, but still couldn't find any seperate function. So I am going to determine two regions, then find their maximum values as peaks. Is this way correct?
My second question is: how to perform Gaussian mixture model with EM in OpenCV? As far as I know, the "cv::EM::predict" function could give me the index of the most probable mixture component. But I have difficulties with training EM. I've searched and found some other codes, but finding the correct parameters is too much difficult for. Could someone provide me any example code for this? Thank you in advance.
#ederman, try {OpenCV library location}\opencv\samples\cpp\em.cpp instead of the web link. I think the sample code in the link is out of date now. I have successfully compiled the sample code in OpenCV 2.3.1. It shouldn't be a problem for 2.4.2.
Good luck:)
My first question is: how can I determine the two peaks?
I would iterate through the range of sample values possible, and test when the does EM.predict(sample)[0] peaks.
I have an image which was shown to groups of people with different domain knowledge of its content. I than recorded gaze fixation data of them watching the image.
I now kind of want to compare the results of the two groups - so what I need to know is, if there is a correlation of the positions of the sampling data between the two groups or not.
I have the original image as well as the fixation coords. Do you have any good idea how to start analyzing the data?
It's more about the idea or the plan so you don't have to be too technical on that one.
Thanks
Simple idea: render all the coordinates on the original image in a 'heat map' like way, one image for each group. You can then visually compare the images for correlation, and you have some nice graphics for in your paper.
There is something like the two-dimensional correlation coefficient. With software like R or Matlab you can do the number crunching for the correlation.
Matlab has a function for this:
Two Dimensional Correlation Function: corr2
Computes two dimensional correlation coefficient between two matrices
and the matrices must be of the same size. r = corr2 (A,B)
In gaze tracking, the most interesting data lies in two areas.
In where all people look, for that you can use the heat map Daan suggests. Make a heat map for all people, and heat maps for separate groups of people.
In when people look there. For that I would recommend you start by making heat maps as above, but for short time intervals starting from the time the picture was first shown. Again, for all people, and for the separate groups you have.
The resulting set of heat-maps, perhaps animated for the ones from the second point, should give you some pointers for further analysis.