Libor

502 reputation

bio	website	componentowl.com
	location	Brno, Czech Republic
	age	27
visits	member for	1 year, 9 months
	seen	2 days ago
stats	profile views	59

Developer of .NET WinForms components and digital photography software.

Currently focuses on ListView replacement component Better ListView,

and authoring a webcomic for geeks.

He loves programming, digital photography, math, travelling and green tea.

	502 reputation	bio	website	componentowl.com	visits	member for	1 year, 9 months
19 badges		location	Brno, Czech Republic		seen	2 days ago

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2d	comment	Optimal sampling for an arbitratry area Thanks. It is not extremely important to have the points distributed the best way possible, just to extend the idea of uniform sampling from rectangular images to the arbitrary shaped areas.
2d	comment	Optimal sampling for an arbitratry area As for the segmentation, I have a clue it may have to do something with Voronoi diagram but I am not sure.
2d	comment	Optimal sampling for an arbitratry area Both answers are acceptable, but inside the shape is better. This is like choosing two points from interval <0,1> - I can choose either {0, 1} or {0.25, 0.75} - both answers are good since I will be working with many (hundreths or thousands) points and treating the border is negligible since only small amount of points will be located near borders.
2d	comment	Optimal sampling for an arbitratry area The problem arises in a field of image processing: Given arbitrary image area, find n sample points that are as descriptive as possible about that area, while not knowing anything about the image content.
2d	comment	Optimal sampling for an arbitratry area The points can be located on borders as well - the only goal is to have the points distributed over the area as uniformly as possible. I think this is somehow related to segmentation problem where each point is a centroid of a segment. In other words, each points should have roughly same space around it so yes, the borders should be repulsive in that way.
2d	asked	Optimal sampling for an arbitratry area
May 9	awarded	Revival
Mar 18	answered	How to fit a curve to my data
Mar 18	answered	Fitting curves to a set of points
Feb 2	comment	Rotating one 3-vector to another I was aware of the first case (very small angle), but you have shown the angle approaching 180° is also important to handle. Thanks.
Feb 2	accepted	Rotating one 3-vector to another
Feb 2	asked	Rotating one 3-vector to another
Jan 30	comment	Normal from multiple vectors Thanks. Both methods work as you said, so I have chosen the one you provided as more numerically stable. Just if you are curious: I have used the method to automatically straighten panoramic image mosaics like this one.
Jan 30	comment	Normal from multiple vectors The vectors are indeed not in the same plane and the system $Ax=0$ is regular, having only one solution which is the undesirable one ($x=\vec{0}$). From what I've read, the least-squares solution is also the right singular vector corresponding to the smallest singular value in SVD of $A$. I think this is the same as the eigenvector corresponding to smallest eigenvalue of $A$. Is that correct?
Jan 7	answered	Gauss Newton minimization of 2D linear function
Jan 7	answered	How to derive the Levenberg–Marquardt algorithm with matrix calculus
Jan 7	answered	Fitting an exponential function to data
Jan 7	answered	Solving an overdetermined system of nonlinear equations
Jan 7	answered	How do I construct the Jacobian for use in a Levenberg-Marquardt algorithm.
Dec 17	comment	Solution to underdetermined linear equations Maybe I am not right, so I picked up the book and updated my answer to put it more in context. Of course, if your original matrix $\mathbf{A}$ have less rows than columns, you can add rows filled with zeroes to have at least a square matrix and proceed with the solution provided in the answer.