This tag is for the mathematics involved in the field of image processing. Many such questions are also appropriate for Signal Processing Stack Exchange.

learn more… | top users | synonyms

3
votes
2answers
58 views

Heat Equation derivative in terms of Laplace

If the heat equation is $ \frac{\partial u}{\partial t} - \alpha \nabla^2 u=0$ Is the second derivative of u w.r.t t is the laplacian of the lapacian?
6
votes
2answers
383 views

Image Reconstruction:Phase vs. Magnitude

Figure 1.(c) shows the Test image reconstructed from MAGNITUDE spectrum only. We can say that the intensity values of LOW frequency pixels are comparatively more than HIGH frequency pixels. $$ ...
4
votes
1answer
87 views

What are Basis images?

I have read that using Fourier transformation we can decompose any arbitrary image into orthogonal basis images and reconstruct it back. But what are basis images actually?
1
vote
0answers
136 views

what does autocorrelation matrix signifies in image processing?

I am trying to find out corners using auto correlation matrix in an image,what does it signifies?
3
votes
0answers
40 views

what is the significance of Eigen values of autocorrelation matrix?

I am trying to find auto correlation matrix of an image to get Harris corners.Paper I am referring suggest that if eigen values of auto correlation matrix are large the point will be corner point.so ...
1
vote
0answers
23 views

Batch Linear Unmixing

Linear unmixing means to solve a set of linear equations to get the proportions of basic elements in the final composit. It is a linear mixture. If we have $f$ features and $m$ basic elements: ...
1
vote
0answers
24 views

Potts model for image analysis

I'm trying to get a hold of the Potts model for image analysis, and this is what is posted on Wikipedia, http://en.wikipedia.org/wiki/Potts_model#The_Potts_model_in_signal_and_image_processing $$ ...
-3
votes
1answer
62 views

Eigenvalues and Eigenvectors of a singular Covariance matrix

I am working on a research in which my data matrix $\bf X$ has dimension of $N\times P$ where $P>>>>N$.ie. its a small sample size problem. I need to compute the covariance of $\bf X$, ...
1
vote
0answers
77 views

Perspective projection alternate matrix (SOLVED)

A lot of perspective projection matrices I've seen look something like this: $$\left [\matrix {1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&z&0}\right]$$ where $z$ is ...
1
vote
2answers
452 views

how to calculate vehicle speed using mathematics and Image processing?

i am doing my project in image processing.using segmentation i have detected the moving part(i.e the car) in the video successfully. But now i want to calculate speed of vehicle. in the above ...
1
vote
0answers
40 views

Is there a way to check if 2D level set function has changed from representing an object of genus 0 to genus 1?

This question has been moved from stack overflow to here. My goal is image segmentation but I think my question is a math one: In computer vision level sets are regularly used to represent moving ...
1
vote
1answer
115 views

Essential mathematics for Image Processing

What are the most essential mathematical concepts one has to be familiar with for succeeding in the field of Image/Signal Processing and Machine Learning. I am somewhat familiar with Tensors, ...
2
votes
0answers
36 views

What is the difference between Bilinear interpolation and Bilinear filtering

I'd like to know that different between bilinear interpolation vs blinear filtering in the manner of image processing warp operation. Are those two operations are identical ? I try to sample a ...
0
votes
0answers
202 views

Looking for a simple algorithm to scale/resize a matrix, or an image.

I am looking for a simple algorithm to scale a matrix of any size. Given matrix A of dimensions [w1,h1]. Given a scaling factor (or resizing factor) SF, which is a real number (not necessarily ...
0
votes
1answer
1k views

Calculating translation value and rotation angle of a rotated 2D image using MATLAB

I have two images which one of them is the Original image and the second one is Transformed image. I have to find out how many degrees Transformed image was rotated using 3x3 transformation matrix. ...
0
votes
1answer
171 views

Hysteresis Image Thresholding

In Image Processing, is it possible to automatically determine the upper and lower levels for a Hysteresis thresholding stage?. I have been looking for a while for a paper mentioning any technique for ...
0
votes
1answer
122 views

Conventional unit mesh

I'm trying to find and outline a non-primitive conventional unit mesh, I'm not sure how to go about it. I'd also like to find any mirrors of planes and rotional symmetry axes. Would this look ...
0
votes
1answer
38 views

Fourier transform in image processing

I want to know what a Fourier transform do to a image, does magnitude of this transform represent the energy of radiations captured by image, or is there any other way to find out the energy of ...
1
vote
0answers
44 views

Euler Lagrange equations

I need to minimise $$\int\limits_\Omega|\nabla H_\epsilon(\phi)|\,dx\,dy$$ with respect to $\phi$. Where $H_\epsilon$ is the regularised Heaviside function, so that it is differentiable. This can be ...
1
vote
0answers
37 views

Non-convexity of an energy functional

How would I go about showing that the following Mumford Shah functional is not convex? $$E_{MS}(u,C)= \int_{\Omega} |u_{0}(x,y) -u(x,y)|^{2}\ dx\ dy + \mu \int_{\Omega \backslash C}|\nabla ...
0
votes
1answer
56 views

Most computationally efficient way to find convolution of a matrix kernel with impulse response?

Let say if we wish to filter an input sequence x[n1, n2, n3] of NxNxN points using an Linear Shift Invariance system with impulse response h[n1, n2, n3], where the filter is a separable sequence, ...
0
votes
1answer
387 views

Looking for a formula to calculate DCT/FFT frequencies when cropping a matrix/image.

Given: A is a matrix of dimensions W1 x H1 . Cropping: Few rows and/or few columns were deleted from matrix A. We got matrix B of dimensions W2 x H2. Not more than 5% of matrix A rows/columns ...
2
votes
1answer
183 views

How does a cropping of a 2D matrix/image affect its DCT transform?

I apologize in advance: since I am not a mathematician, maybe my question is not well defined, but I hope that some of you will still understand my meaning. Given a 2D matrix, or an image of ...
1
vote
0answers
37 views

Rigid Deformation

I'm trying to parse through this paper on using the method of moving least squares for rigid transformations - http://www.cs.rice.edu/~jwarren/research/mls.pdf Under section 2.3, the author mentions ...
1
vote
1answer
73 views

Why we take transpose of Vector (Displacement Vector)?

I'm trying to understand some equations that involves transpose of vectors (displacement vectors to be precise) Two set of vectors F and G (with i,j) that corresponds to X,Y value in plane and ...
2
votes
0answers
46 views

Regularized least squares

In Image Restoration, a true image $f$ (in vector form) can be related to degraded data $y$ through a linear model of the form $$y = Hf + n$$ where $H$ is a 2D blurring matrix and $n$ is a noise ...
3
votes
0answers
24 views

Detecting camera shake

I have a bunch of data captured from a worm tracker that consists of a B&W camera that stares down at a few dozen worms for an hour at a time. The tracker captures the outline of each worm ...
1
vote
0answers
58 views

Image histogram equalization using variational calculus

In an image processing course at Coursera.org, on the section on PDE and calculus of variations, the professor gave the following as the functional to be optimized for image histogram modification: ...
2
votes
2answers
74 views

Is it possible to formalize areas such as image processing and computer vision?

Is it possible to formalize areas such as image processing? By formalize I mean setup axioms, then derive theorems, and reason about image processing concepts and methods formally. I would say now ...
1
vote
1answer
186 views

texture mapping from a camera image to a 3D surface acquired by a kinect

I have the following problem: A kinect camera capture a 3D surface and save it as a .obj files containing all the positions of the vertices (in the kinect coordinate system). If I take a picture ...
0
votes
1answer
47 views

how to introduce time into calculus of variations for image processing?

I'm studying some topics about calculus of variation applied to image processing. I'd like to understand how to introduce time parameter to evolve an image in an iterative way. For example, let's ...
4
votes
1answer
1k views

How can I combine affine transformations into one matrix?

So from what I understand from this picture, the box is stretched to twice its width. And it is then flipped from the x-axis. And then it is rotated 30 degrees anticlockwise. So these three ...
1
vote
0answers
41 views

Which figure provides the greatest change in angle per change in distance? (trigonometry)

I have been having a lively discussion with others about the following: We (myself and others) are using triangulation to measure distance to an object with a linear image sensor (CCD) and a ...
0
votes
1answer
345 views

Gaussian distribution and its parameters

I need to learn more about Gaussian distribution and given a set of data, plot a Gaussian distribution of it. Using the following code sample, could you please tell me how I can plot a Gaussian ...
2
votes
1answer
184 views

Texture mapping from a camera image (knowing the camera pose)

I'm not sure if I should ask this question here or on stackoverflow, so forgive me if I'm wrong. I want to apply a texture (taken from a camera) on a 3D surface, let me explain my problem: I have ...
1
vote
0answers
282 views

Area optimization: Packing rectangles inside rectangle

Background: I am scrambling to figure out the optimization algorithm to build sprite image, which is essentially a big container rectangular image, with multiple rectangular images. I have found an ...
2
votes
1answer
605 views

Mathematical Background for Computer Vision [closed]

I am a PhD student and would like to do deep research in the area of computer vision and pattern recognition. I know to be successful I need strong mathematical background. Could you please introduce ...
0
votes
0answers
28 views

Convolution of an image with a kernel that is a product of two functions

Suppose that $G(i,j)$ is a Gaussian decay function on the distance between points $i$ and $j$ of an image. In addition, $D(i,j)$ is the difference between the VALUES of the image at those points. ...
0
votes
3answers
253 views

Calculating the next value of sin(x) from previous sin.

(Please bare with me as I try to explain my problem to the best of my abilities) I have a computer program that draws a sine. Each y value of the sine is stored against the x value in an array like ...
1
vote
1answer
104 views

fitting the content of an elliptical region in an image into the equivalent stretched circle

Assuming that I know the ellipse parameters (the major/minor axis, theta and the centre), and I could get the equivalent circle of this ellipse (I mean the equivalent x and y positions of the pixels ...
1
vote
1answer
223 views

circle affine transformation

I am trying to convert a region of pixels surrounded by an ellipse into an equivalent stretched circle.This basically means affine transformation. Assume I want to extract the region in light blue ...
2
votes
1answer
74 views

Poisson equation with dirichlet condition

I'm not sure whether this is a mathematics or stack overflow question, but I'll try here as my doubt are because of my lack of maths knowledge. I'm trying to implement an image editing paper that ...
2
votes
4answers
2k views

PCA - Image compression

I have 2 questions related to principal component analysis: The first is, how do you prove that the principal components matrix forms a orthonormal basis? Are the eigenvalues always orthogonal? The ...
3
votes
3answers
268 views

How to calculate the size of any rectangle to fit into an ellipse?

It's been a long time I do not review my math knowledge, please help me out. I have an ellipse image with fix size, let's say it has the bounding rect with width=w1, height=h1, and I have any random ...
0
votes
3answers
59 views

Getting $x,y$ position on an image based on given value

This should be simple but my math skills are really bad ... I have an image of 36 images (6 by 6 matrix). These small images are 36 instances of a direction arrow (like from Google maps GPS), each ...
0
votes
1answer
55 views

Help with least squares in paper on hough transform

I'm trying to understand this paper. I'm having trouble with a least squares problem. In the paper, equation (4) is $ E^2 = \sum_{r\in R}{\sum_{c \in C}{[ \alpha r + \beta c + \gamma - I(r,c)]^2 ...
1
vote
0answers
45 views

What are interesting ways to tile a square image? Or a transformation that make an image tilling-able?

I want a method to tile arbitrary square image. For most cases the boundaries do not agree. So I are looking for a transformation from a square image to a square image whose boundaries agrees. One ...
0
votes
1answer
239 views

Gradient of a norm with a linear operator

In mathematical image processing many algorithms are stated as an optimization problem, where we have an observation $f$ and want recover an image $u$ that minimizes a objective function. Further, to ...
0
votes
1answer
92 views

Proportional Image Resizing

This is quite a simple one I guess (but my mind is dead currently and is getting cluttered by other numbers). I have an square image that is currently 256 width x 256 height. I am variably resizing ...
1
vote
1answer
281 views

Huffman Coding Integer Identifier Table

this might be trivial but I have a brainfog here! I am working through a JPEG compression problem using Huffman codes. According to our book, the process for coding a quantized matrix for a jpeg has ...