Rank: 485 based on 242 downloads (last 30 days) and 5 files submitted
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Anton Semechko

E-mail
Company/University
University of Toronto
Lat/Long
43.6615, -79.395

Personal Profile:

PhD student

Professional Interests:
Signal/medical image processing, computational anatomy and biomechanics

 

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Files Posted by Anton View all
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(last 30 days)
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30 May 2013 Screenshot Fast segmentation of N-dimensional grayscale images Partition N-D grayscale image into c classes using efficient C-means and fuzzy C-means clustering Author: Anton Semechko image segmentation, fuzzy cmeans, cmeans, kmeans, clustering 66 2
  • 5.0
5.0 | 1 rating
23 May 2013 Screenshot Uniform Sampling of a Sphere Create an approximately uniform triangular tessellation of a unit sphere Author: Anton Semechko thomson problem, particle system, uniform sampling of a..., subdivision, triangular quadrisect..., optimization 69 12
  • 5.0
5.0 | 4 ratings
29 Jan 2012 Screenshot Nonlinear Relaxation Labeling for Image Processing Improve spatial coherence of a 2D monochromatic/multispectral image using probabilistic relaxation Author: Anton Semechko nonlinear relaxation ..., relaxation labeling, relaxation labelling, probabilistic relaxat..., image segmentation, image regularization 28 3
  • 5.0
5.0 | 1 rating
23 Jan 2012 Screenshot Decimate Polygon Simplify a 2D closed, piecewise linear contour by specifying boundary offset tolerance. Author: Anton Semechko polygon simplificatio..., polygon decimation, image processing, simplify polygon 36 8
  • 5.0
5.0 | 2 ratings
07 Jan 2010 Screenshot EXACT HISTOGRAM SPECIFICATION/EQUALIZATION Exact histogram specification/equalization for 2-D monochromatic images. Author: Anton Semechko exact histogram speci..., exact histogram match..., exact histogram equal..., histogram matching, histogram specificati..., histogram equalizatio... 43 4
  • 4.75
4.8 | 4 ratings
Comments and Ratings by Anton View all
Updated File Comments Rating
24 Jun 2014 subtightplot Asymmetric subplots with variable inner gaps and outer margins. Author: Felipe G. Nievinski

12 Jun 2014 Minimum Volume Enclosing Ellipsoid Computes the minimum-volume covering ellipoid that encloses N points in a D-dimensional space. Author: Nima Moshtagh

sweet, thanks!

30 May 2014 A suite of minimal bounding objects Suite of tools to compute minimal bounding circles, rectangles, triangles, spheres, incircles, etc. Author: John D'Errico

Hi John, I sent you an e-mail to the electronic address provided on your Matlab profile. In that e-mail I attached a point cloud for which 'minboundsphere' fails almost consistently.

28 May 2014 A suite of minimal bounding objects Suite of tools to compute minimal bounding circles, rectangles, triangles, spheres, incircles, etc. Author: John D'Errico

Hi John, I ran your 'minboundsphere' function a number of times (for 8 different meshes) and observed that occasionally it fails to produce a minimum bounding sphere that encloses all of the points. In some of these cases, the distance for 5% of the points is a factor of 1.1 greater than the computed radius.

27 May 2014 A suite of minimal bounding objects Suite of tools to compute minimal bounding circles, rectangles, triangles, spheres, incircles, etc. Author: John D'Errico

Thanks John! Great submission. I found your function to find minimum bounding spheres especially useful.

Comments and Ratings on Anton's Files View all
Updated File Comment by Comments Rating
10 Apr 2014 Uniform Sampling of a Sphere Create an approximately uniform triangular tessellation of a unit sphere Author: Anton Semechko Semechko, Anton

Hi Zara, I am glad you found this submission useful. Unfortunately there is not white paper to accompany this submission. Therefore, it is entirely up to you how and if you choose to cite this.

09 Apr 2014 Uniform Sampling of a Sphere Create an approximately uniform triangular tessellation of a unit sphere Author: Anton Semechko Zara

Hi Anton,
Thanks a lot for your nice code. It helped me a lot. How can we cite your work? Just an acknowledgement?

07 Apr 2014 Uniform Sampling of a Sphere Create an approximately uniform triangular tessellation of a unit sphere Author: Anton Semechko Manuel

Hi, I clearly misunderstood the matlab function 'convhulln' here is a nice explanation of it:

http://www.mathworks.com/matlabcentral/answers/9298-pretty-simple-question-regarding-convhulln-now-that-i-have-k

07 Apr 2014 Uniform Sampling of a Sphere Create an approximately uniform triangular tessellation of a unit sphere Author: Anton Semechko Manuel

Hi Anton, Thank you for your soon reply. You are right I did not know that result of triangulation grows exponentially with number of dimensions (n), as you nicely illustrated with the random 100 points, so just for n=20 ‘convhulln’ will return an array of doubles with roughly 8.8E+12 elements and to store that I’ll need 65 400 GB of RAM. I only have 125 GB ☺. What is interesting here is that I do not get matlab ‘out of memory’ error but instead ‘The data is degenerate in at least one dimension – ND set of points lying in (N+1)D space’ . The good news is that I don’t really need to triangulate the points (I don’t need to know indices of the points that comprise the facets of the convex hull) even though it could be used to make sense of the data by sampling some areas and comparing them for instance. Well this takes the function ‘convhulln’ out of the game.
But, how about your code? Why are you amazed it worked for 525D? It basically addresses an optimization problem in 3D that can be for sure addressed in higher dimensions too (perhaps using a more sophisticated scheme like Conjugate gradient, etc). Well the thing is that you have done it and shared it, which all of us appreciate, and I am trying to expand its applicability.
Coming back to the hyper sphere in 525D, I don’t know how such a surface looks like ☺ but I believe that 3 points in a hyper dimensional space will define a triangle (just as they do in 2D and in 3D) so approximating the surface of an hypersphere with a set of triangles makes sense to me, therefore I wonder what do you mean by: “… 525 dimensional convex hull is a terribly poor approximation to a hypersphere…”
Once more thank you for your comments and no, I am not kidding!

06 Apr 2014 Uniform Sampling of a Sphere Create an approximately uniform triangular tessellation of a unit sphere Author: Anton Semechko D'Errico, John

Manuel - You apparently have NO idea how complex a triangulation of the surface of a 1000 dimensional hyper-sphere will be. The result would be IMMENSE.

In fact, I'm amazed that it succeeded for dimension 525. For example, try computing the convex hull of a fixed number of points on a hypersphere, what happens?

xyz = randn(100,2);
xyz = bsxfun(@rdivide,xyz,sqrt(sum(xyz.^2,2)));
t = convhulln(xyz);size(t)
ans =
100 2

xyz = randn(100,3);
xyz = bsxfun(@rdivide,xyz,sqrt(sum(xyz.^2,2)));
t = convhulln(xyz);size(t)
ans =
196 3

xyz = randn(100,5);
xyz = bsxfun(@rdivide,xyz,sqrt(sum(xyz.^2,2)));
t = convhulln(xyz);size(t)
ans =
1936 5

xyz = randn(100,7);
xyz = bsxfun(@rdivide,xyz,sqrt(sum(xyz.^2,2)));
t = convhulln(xyz);size(t)
ans =
24266 7

xyz = randn(100,9);
xyz = bsxfun(@rdivide,xyz,sqrt(sum(xyz.^2,2)));
t = convhulln(xyz);size(t)
ans =
287356 9

This last one started to take a significant amount of time, as you might expect.

Anyway, that 525 dimensional convex hull is a terribly poor approximation to a hypersphere. You are kidding yourself.

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