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

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What would the derivative of this objective function be?

My question comes from image processing community, In our Machine Learning algorithm, we have a predicted value $D$ and its equivalent ground truth $D^*$ where their difference is: $d_i=D-D^*$. (...
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43 views

represent an image in linear algebra

Can we represent a grayscale image as a matrix of values, and then apply all our linear algebra techniques to that? Like finding the column space and null space, reason about the matrix structure. ...
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What does it mean to project all rotations of a function onto a different function?

Steerable filters allow me to optimally select an orientation of a filter without iterating over the set to find the optimal response (I'm doing this with a computer). The exact words from the paper ...
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27 views

Applying distortion to Bézier surface

I am trying to simulate the image warp effect, that is used in Adobe Photoshop. The rectangular image is warped according to a cubic Bézier surface (in 2D, all Z components are 0). Having any Bézier ...
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16 views

Calculation for getting dimension of object in image not working

I am trying to calculate the dimensions of an object in an image. This is a sample image I took to get height of blue shirt: image of blue shirt I am following the math from this page with sastanin'...
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6 views

How to find a basis function of 2d zero mean template function

Given a 2d zero mean template $t^{'}\left ( x,y \right )$, and $\sum_{x=0}^{u-1}\sum_{y=0}^{v-1}t^{'}\left ( x,y \right )=1$, $\bar{t^{'}}(x,y)=0$ How to expand the $t^{'}\left ( x,y \right )$ ...
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76 views

I am looking for a mathematical equation to warp an image [closed]

Theoretically, I know that to warp an image, each pixel $(x,y)$ in the source image is transformed to $(x', y')$ using a function f (i.e. $x'=f(x,y)$ & $y'=f(x,y)$ ). But what mathematical ...
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14 views

gradient of total variation norm in total variation denoising

I am learning total variation denoising. The gradient of TV norm need calculated. From the link: http://www.numerical-tours.com/matlab/denoisingsimp_4_denoiseregul/ It says that the gradient is ...
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1answer
21 views

Is there any approach to computer vision that doesn't make use of geometry?

I've long been interested in applying my background in functional analysis (especially wavelets) and other related areas to actually create something with "real world" value (not that I don't enjoy ...
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13 views

What different between huffman and EBCOT?

I have a question about entropy coding and Image compression. Huffman coding and EBCOT coding are entropy coding. correct or not? I knew about huffman coding but I don't know EBCOT, How it working?...
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45 views

Compute two 1D lookup tables for computing DCT of a 2D Laplacian

I am following a paper that I have to implement through coding and I am struggling understanding what it means exactly with the sentence "create two 1D lookup tables for computing the DCT of a 2D ...
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8 views

Morphological operations with even sized structuring elements

The well-known morphological operations, such as dilation/erosion, opening/closing, top-hat... , widespread in digital image processing, are defined by means of so-called structuring elements. For ...
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9 views

Phase correlation vs. normalized cross-correlation

In 2-dimensional discrete signal analysis (specifically image processing), a definition I found for the normalized cross-correlation between two images, both of size MxN $g_1(x, y)$ and $g_2(x, y)$ is:...
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3answers
71 views

Maximum Eigenvalue of the Discrete Laplace Operator (Image Processing)

Given the derivative operator in image processing $$ A = \begin{bmatrix} 1 & -1 & 0 & 0 & \ldots & 0 & 0 & 0 \\ 0 & 1 & -1 & 0 & \ldots & 0 & 0 &...
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31 views

Estimate original matrix from matrix multiplication result

Let $A$ be $m \times n$ real matrix. Let $B$ be $n \times k$ real matrix. Let $C= A \times B$ ($m \times k$ matrix). Now, the question is: given $C$ and $A$, give an estimate for $B$. Possible ...
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42 views

Alignment of one 3D Coordinate system to another 3D Coordinate system

I'm working on a project depicted by this picture(taken from internet) where there are different coordinate system involved which corresponds to camera coordinate system and local 3D coordinate system ...
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34 views

recursive least squares for nearly singular matrices

I have an image reconstruction problem which I want to solve as a linear system $Ax=y$. A matrix is big, but for the beginning I can shrink the imaging region to $nPix$ = 2000 pixels. number of ...
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14 views

Thinning vs. medial axis transform

Both thinning and medial axis transform of a binary image produce a simplified version of the image, reducing the connected components to single-pixel wide subsets, also called skeletons. The one ...
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1answer
26 views

Minimizing $ E(q)=\lambda(q-p)^T(q-p)+q^TLq $

Let $ E(q)=\lambda(q-p)^T(q-p)+q^TLq $, where $\lambda$ is a scalar, q and p are n by 1 column vectors, L is an n by n positive definite matrix (Actually Laplacian matrix, in image processing field)....
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When is a mapping the proximity operator of some convex function?

Sorry for cross-posting from MO. It's been a few days and the question hasn't received any attention there. So, is there a characterization of mappings $p : \mathbb R^n \rightarrow \mathbb R^n$ which ...
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14 views

What are kernel space, functions and data?

I'm reading Kernelized Locality-Sensitive Hashing, which is obviously based on the concept of kernel applied to space, functions and data. It seems particular relevant in image processing domain, but ...
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1answer
61 views

Geometric explanation of a methodology in the article about Image Denoising

In article Ghimpeteanu G., et al. - A Decomposition Framework for Image Denoising Algorithms, I found as below: Let $\displaystyle I : \Omega \subset R^2\mapsto R$ be a gray-level image, and $(x, ...
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19 views

Learning point spread function image processing

Given a set of images, that are blurred by Gaussian point spread function, how can I learn the parameters of the PSF, i.e. standard deviation of the Gaussian kernel. One way that I can think of is to ...
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19 views

How to represent the function of variables?

I have a function as $$E=\int_\Omega -\log\big( p_i(x)\big) dx$$ where $p_i(x)$ is density distribution which estimated by Parzen window method. $p_i(x)=\frac{1}{\Omega_i} \int_{\Omega_i}K_\sigma\big(...
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39 views

Determinant of Hessian approximation

I have a question regarding formula in SURF article by Bay et al. Theory Given a point $p=(x,y)$ in an image $I$, the Hessian matrix $\mathcal{H}$ in $x$ at scale $\sigma$ is defined as follows $$ \...
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26 views

Image processing, optimization via regularization - efficient strategy

i would like to solve the following system: $J(x) = |Ax-b|_2^2+\gamma|\nabla x|_2^2$ subject to: $x \geq 0, \sum_i x_i = 1$ The underlying problem is to derive the PSF from a sharp and blurry ...
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15 views

To get boundary of xy coordinates around object inside an image using active contour method

Trying to extract the XY coordinates around the boundary of an lesion object inside an image of plain background. I am using the active contour method as suggested to find x and y coordinates along ...
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2answers
57 views

Largest four line segments of polygon

I have some polygon (see darkblue contour): It consists of very small segments, pixel by pixel, so angles differ although they seem to be the same. Visually we see 4 large line segments. How can I ...
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2answers
61 views

An algorithm for finding the intersection point between a center of vision and a surrounding rectangle

In plane $\mathbb{R}^2$, a rectangle $R$ with center $P_2(x_2,y_2)$ and vertices $(x_2 \pm w, y_2 \pm h)$ (sides parallel to axes) is given. We consider the transformation which, to a given point $P_1(...
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29 views

Contour and perimeter recognition in binary image

I need to detect contour (object) and find the perimeter of a detected object. For example, I have the following image: http://i.stack.imgur.com/40TTX.png All images are binary, so they consist of ...
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45 views

Relation between focus and camera intrinsic parameters

Does a focus tuning affect the camera intrinsic parameters? More precisely, if the focus of a camera is changed, does the camera intrinsic parameters matrix remain unchanged? Apparently, since this ...
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Does the ring in this Fast Fourier Transform image of a hexagonally close packed structure have significance?

I have a picture of a hexagonally close-packed lattice and I took the FFT of the image using ImageJ. Below are the results. I expected the FFT to also be a lattice with reciprocal lattice spacing, I ...
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I downloaded the SPARCO package (MATLAB)and when setting it up a problem has occured

I downloaded SPARCO1.2 (MATLAB) from http://www.cs.ubc.ca/labs/scl/sparco/ and when I use the command 'sparcoSetup' it says everything is successful. But then when I use the command 'checkProblems' ...
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10 views

Number of operations in convolution of an image with a sequence of kernel

In the vein as this question, I'm trying to see how many operations convolution takes (in the context of image processing), as illustrated by the following GIF: I'm interested in the naive ...
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27 views

Distance between a map and a point using bicubic interpolation

I have an image (i.e., a two dimensional regular grid) with pixel values that represent elevations. To interpolate points of the surface described by the grid, I use bicubic interpolation. The image, ...
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16 views

Transformation between camera velocity and projection of a tube's cut

I have a vision sensor / flying camera inside a circular tube as shown below: The camera is using the pinhole model and I am using edge detection to detect the "black" hole that is forming due to ...
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1answer
47 views

Calculate if image dimensions are too horizontal or vertical

I'm working on a PHP script that adds images to articles automatically. A common problem I've encountered is that the image dimensions can be too wide or too tall. In terms of aspect ratio of wide ...
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1answer
58 views

Method for finding basis of an image

I know the traditional method for finding an image of a matrix is finding the pivot columns of the rref of the matrix and then the corresponding columns are the basis of the image, but I'm wondering ...
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1answer
70 views

Pyramidal Histogram Of Oriented Gradients - Trilinear interpolation

Hello im struggling with an implementation of this article: https://goo.gl/8mpIuq I performed bilinear interpolation over the histogram bins and the results are better with this interpolation, ...
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15 views

determine the absolute difference in bits between using an indexed colour

Given the following 4 x 4 image, determine the absolute difference in bits between using an indexed colour (where the index uses the lowest number of bits possible, but the colour is represented as ...
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18 views

finding image and kernel from convolution result

given a one dimension image/(signal) I and three kernels K,L,J. given the results of the convolution of I with each kernel, for example \begin{matrix}I*K =[ 1/3&2/3&1&1&1&1&1&...
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1answer
72 views

Fourier transform of a 2D image, and noise cancelation

I'm a statistics grad student, and I just started getting into Digital-Image-Processing (an analogy for processing super-large contingency tables). In the book "Digital Image Processing" by Gonzalez ...
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1answer
29 views

SVD for Seam Carving

Could SVD be used for Seam Carving ? I am making a small program for a uni course and I'm looking for different ways to calculate pixel energy; which made me come across SVD. Among others, I have ...
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25 views

Temerature and Strain images comparison & interpolation: finding offsets in X,Y coordinates systems.

I have two kind of 2D images from a Strain test, which show temperature and strain distributions in X and Y cordinate systems. One is thermal image, which gives temperature T values in a 200x300 ...
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Derivative of an Euclidean-Vector norm.

Consider: x a $N \times 1$ vector , with elements $x_i$ b a $N \times 1$ vector , with elements $b_i$ A a $M \times N$ matrix , with elements $a_{ij}$ ( Symmetric matrix - Block Circulant ) As we ...
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How do you take the discrete Fourier transform (DFT) of a parallelogram or a Bravais lattice in general?

I'm working on implementing a method that extracts the corresponding wallpaper group given a gray-scale image/pattern. But to do so, I need to take the DFT of a unit cell in the image which, in the ...
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22 views

Filtration on simplicial complex as a grayscale image

If we make a filtration on the complex built from vertices and edges and faces(2dimensions) of a grayscale image according to grayscale value. Does it considered as a filtration on simplicial complex? ...
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1answer
34 views

Homography with line correspondences

When calculating a homography with line instead of point correspondences, what is the derivation of the formula: $$ l_i = H^T\cdot l^{'}_i $$ I know that: $$ l^T\cdot x = 0 \quad\text{and}\quad l^{'...
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2answers
80 views

How/why does matrix multiplication work to do a linear fit? [closed]

Some background: I have a B.S. in physics. I have taken linear algebra. I do work that involves doing image analysis in IDL. One thing I have to do a lot is fit a linear equation $(y=mx+b)$ to the ...
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30 views

Explanation of Template Matching formula

Can someone please explain the formula f.) on OpenCV template matching Formula: Suppose template image is 3x4 and source image is 15x20 how would the mathematical operations follow...