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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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
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0answers
22 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 ...
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0answers
50 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
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2answers
71 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 ...
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1answer
151 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 ...
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1answer
39 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
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1answer
781 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 ...
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0answers
39 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
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1answer
290 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
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1answer
149 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 ...
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0answers
222 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
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1answer
511 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
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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. ...
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3answers
251 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 ...
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1answer
94 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 ...
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1answer
185 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
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1answer
73 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
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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
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3answers
193 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 ...
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3answers
54 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
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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 ...
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0answers
40 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
224 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 ...
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1answer
84 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 ...
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1answer
249 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 ...
3
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1answer
267 views

May I know how to solve this Huffman coding-related question?

Question 1: An image is coded with 3 bits per pixel and the probabilities associated with each of the grey levels are P = [0.2 0.15 0.13 0.13 0.12 0.10 0.09 0.08]. (i) Using ...
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2answers
27 views

Data preprocessing

How would you preprocess 2 dimensional data to have 0 mean? Say you have a matrix $M $ that is $p \times q $. Would you calculate the mean of each row, get a vector of length $q $ and subtract each ...
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0answers
160 views

Whitening matrix for Fast ICA

I have a matrix $X $ with dimension say $ m \times n $ with $ m> n $. I am trying to whiten this matrix in matlab by first taking the $C= \operatorname{covariance}(X)$ followed by eigenvalue ...
3
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5answers
319 views

How do I find/predict the center of a circle while only seeing the outer edge?

Question What formula would allow me to predict the center of this circle? In addition, what attributes of this image must be detected in order to predict the center? I figured understanding the ...
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1answer
50 views

Omitting part of Frequency domain, Fourier Transform, Image Processing

In my Image and Signal Processing lecture, the Professor said that if every other column of the frequency domain of an image is zeroed out, then the reconstructed image is aliased. (along the x-axis) ...
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0answers
62 views

Anamorphotic Projections onto Awkward Solid Surfaces

I have been experimenting with some 19th century picture development techniques that involve photochemical image projection: For flat pictures you first mix equal parts of chemicals like ferric ...
0
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1answer
171 views

How to interpret the results of 2D Fourier Transform on an image?

I have a class where we're studying signals processing (mostly filtering of sounds and images) and while I kind of understand the results of a Fourier Transform for sounds I don't really get the ...
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2answers
195 views

Mathematical explanation for image edge detection and denoising

I am trying to understand why the convolution kernel, $$\left[\begin{array}{rrr} -1&-1&-1\\ 2&2&2\\ -1&-1&-1 \end{array}\right]$$ detects the edges in an image. If anyone has a ...
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0answers
128 views

How to show that the Harris corner detector is rotation invariant

I understand what it means for the Harris corner detector to be rotation invariant. But what steps do you need to take to show that it is rotation invariant?
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1answer
42 views

understanding bases and frames for Gabor transform

For the 2D discrete Gabor transform, why is it that we cannot use a set of orthonormal basis for its representation, instead we have to use frames for representing it?
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3answers
376 views

Principal Component Analysis in Face Recognition - number of Eigenvalues?

I'm at the beginning of learning about the PCA as it is applied in the field of face recognition (Eigenface algorithm) and I came about the following question: "You're using a training set of 80 ...
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2answers
353 views

How to convert coordinate system of java image to conventional coordinate system?

I am working on some image processing problem. So I am facing a problem that in java the coordinate system of image is not like the conventional coordinate system used in Mathematics (where origin is ...
0
votes
1answer
81 views

How to find the screen-coordinates of the robot facing diagonally on the screen?

I am participating in a national robotics competition called "National Robosprint Pakistan". I have designed a robot which can move forward, backward and change its angle where it is facing. Actually, ...
2
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2answers
782 views

normalized Laplacian of Gaussian

Laplacian of Gaussian formula for 2d case is $$\operatorname{LoG}(x,y) = \frac{1}{\pi\sigma^4}\left(\frac{x^2+y^2}{2\sigma^2} - 1\right)e^{-\frac{x^2+y^2}{2\sigma^2}},$$ in scale-space related ...
0
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1answer
1k views

Undecimated Wavelet Transform (a trous algorithm) - how to determine 'anchor'/'center' of convolution filter

i am currently implementing the 'Undecimated Wavelet Transform' with the 'a trous' algorithm. See e.g. http://www.znu.ac.ir/data/members/fazli_saeid/DIP/Paper/ISSUE2/04060954_2.pdf, section II-A. As ...
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1answer
642 views

kernels to compute second order derivative of digital image

For an image $I$, its first order derivatives can be computed using several oprators, such as $$K_{sobel} = \left[ \begin{array}{ccc} -1 &0 &1 \\ -2 &0 &2 \\ -1 &0 &1 ...
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0answers
92 views

Keeping a constant resolution scale of an image

Intro I'm writing a program that zooms in and out on an image and the only way to do it with the data I have is to change the limits of my graph. The aspect ratio (scale of x to y) always remains 1:1 ...
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votes
1answer
204 views

Calculations multiple images to resize proportionally?

I am not sure about the title of this question. I have multiple images in one canvas. The first image is a background. The other images is in a dynamic position by the background image. I want to ...
3
votes
1answer
140 views

Minimization problem as PDE

In the article "An Image Interpolation Scheme for Repetitive Structures" Luong, Ledda and Philips propose the following approach to denoising digital image. They consider that regularized total ...
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1answer
151 views

FFT of a matrix and its square.

I am doing something computationally intensive that requires that I compute the fast fourier transform of a matrix, let's say $A$, and also compute the FFT of its square, $A^2$. I am wondering if ...
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votes
1answer
232 views

Extract and then insert back a sub-block of a picture using matlab [closed]

I have a picture as an input to matlab $(256\times256)$: img=imread('cameraman.tif'); I want to embed a watermark using a spatial domain method. For this purpose i choose a random sub-block of ...
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2answers
48 views

Translate a line from a whitepaper to English

I'm attempting to implement an image processing algorithm from this white paper (p. 5), but I'm having difficulty with the math jargon, in particular this line: ...
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1answer
32 views

For a given image $\mathbf X$, the equivalence class for pixels $p$ with labels $l$.

$\left[l\right]=\left\{p \in\mathbf X|\,p\sim l\right\}$. This is taken from this paper on image segmentation, page $2$. I don't know how to interpret this, do they mean "all the pixels on image ...
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0answers
89 views

viewing ray geometry - with multiple aerial photographs

I am working with multiple aerial images. My idea is to model 3d objects (only upper parts). I am having known orientation parameters. As I am new to this field so that, I want to clarify few general ...
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0answers
236 views

Produce a 4:2:2 sub sampled Y matrix, Cr matrix, Cb matrix for an image

I have write the matlab code below for to extract Y, Cb, Cr information from the picture: ...