Recent content by pamparana

I am taking a course on linear regression online and it talks about the sum of square difference cost function and one of the points it makes is that the cost function is always convex i.e. it has only one optima. Now, reading a bit more it seems that non-linear functions tend to give rise to...

Can someone recommend some background texts which can build me up with the necessary pre-requisites to learn about Riemannian Geometry? I have been self studying single and multi variable calculus but lack the mathematical rigour. Some resources/textbooks that can cover the background material...

Thanks for that explanation. As far as I understood, the optimisation is going (well, according to some local minima/maxima) to select the best rotation function which optimises the given cost function. So, in this case \theta can be seen as a variable as we evaluate the cost function by varying...

I have a small confusion about functions and variables. So, on doing a bit of reading, a linear transformation is a function that maps inputs from one vector space to another. So, let us take for example a simple rotation matrix. This matrix takes a point in 2D space and maps it to another...

Thank you for this detailed answer!

I just wanted to check something. If I have a complex number of the form a = C * \exp(i \phi) where C is some non-complex scalar constant. Then the phase of this complex number is simply \phi. Is that correct?

Yeah, sorry I know it might be slightly confusing. In image processing, people tend to use i for an index or location. Yes, i is a constant and is a spatial location in the space of the reference image and whole corresponding location in the other image is given by t(i, w), which is the...

The map is 1-1 i.e. bijective. The cost function is basically encapsulated in the integral as the sum of square difference, so we assume the errors in matching are normally distributed, which is what the exponential term is telling us. The issue for me is not to do the transformation/mapping...

Sorry my notation is not probably very clear. I am more of a software engineer and have not had a math class in a good 30 years! So, let us just talk in terms of one dimensional images. So, the images are usually sampled on a uniform grid at discrete locations but I will assume that an image...

Thanks for the reply! They are transformation parameters but are treated as random variables and hence have a distribution associated with them. I am trying to compute the posterior distribution associated with the transformation parameters w i.e. P(w). So the integral expression comes from...

I started a new thread, with hopefully more helpful information, here: https://www.physicsforums.com/showthread.php?t=756381

I will give a small background and explain the variables and the system first. I have two images which are observed and are constant and we can treat them as continuous functions and I will call them r and f. In my problem, I am trying to find a continuous transform (which is very non-linear)...

I will start a new thread about this as things will get confused perhaps. I will try and generate an expression for t using some interpolation function.

I was wondering if I can assume that t varies slowly, if this could help with this integration in some way. So, I can assume that t is a smoothly changing function and can be differentiated infinitely even. Would that help in solving this integral?

Yes, typically each 3D point in the space of image x is moving to another 3D point in the space of image y. The problem is regularised in some way but the function is still highly non linear with many local minima possible and quite severely under-determined. So, I guess I am a bit stuck here.