This tag is for the mathematics involved in the field of image processing.

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Rearranging convolution equation: seismic image processing

I am looking at the theory of surface related multiple elimination and I have got to a point where it says: If we define an operator $a(t)$ as follows $$a(t) \ast s(t) = - \delta (t),$$ ...
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1answer
45 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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59 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 ...
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1answer
120 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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0answers
68 views

Moving from 1D to 2D space

In 1D space I can create a Gabor function $h(x)$ as the product of a sinusoid and a Gaussian envelope $ f(x) = sin(2\pi x)\\ g(x) = e^{-\frac{(x-x_0)^2}{2\sigma^2_x}}\\ h(x) = f(x)g(x) $ What I ...
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2answers
158 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
102 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
37 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
308 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
270 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 ...
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1answer
62 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, ...
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2answers
438 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 ...
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1answer
714 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
469 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
82 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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1answer
164 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
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1answer
105 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
106 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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1answer
155 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
47 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
31 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
84 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
132 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: ...
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2answers
895 views

Scale Space - Scales and Octaves

So I'm desperately trying to understand scale space for signals, specifically for 2D images... I'm having trouble with algorithms that discuss creating a pyramid. Specifically, I don't understand how ...
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1answer
89 views

How to solve cross-products including matrices?

I'm a programmer and I'm doing a whitebalance-transformation in RGB colorspace. This should work with this transformation matrix that I've found in literature: $$ \begin{pmatrix} R \\ G \\ B ...
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1answer
109 views

Unclear on relationship between different dimensionalities of Fourier transform

This is probably a silly question, but it's one that's directly relevant to a project of mine and I figured this was the place to go. I have some objects that contain a 1d and a 2d array of double ...
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2answers
182 views

intensity transformation 16-bit image to a 8-bit image

Give an intensity transformation function T for converting a 16-bit image to a 8-bit image, i.e. T takes an integer from {0,1,2,...,65535} and returns an integer from {0,1,2,...,255}. Can we use $s = ...
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1answer
229 views

A Mathematical way to represent a image kernel?

How to represent the calculation in this image mathematically? For example: With the discrete convolution and Fourier Transform. It tries to do a calculation on the original image (image A/input) ...
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1answer
44 views

How to estimate orientation errors of an image with respect to known data (line features)

I think this is very simple but for me, it is confusing to figure out a way. Here is my problem. I have been given a 3d line segment list obtained from a field survey. So I know each end point ...
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1answer
75 views

obtainig a line 3D from multi view geometry

If I have been given multiple view images having known orientation parameters, then from a selected image line segment (corresponding line segments from each image) how could I compute a line 3D in ...
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1answer
453 views

Minimizing mean squared error

I want to find a $d$ that minimizes the value of the expression below. I think the first step is to find the derivative w.r.t. $d$ (is that correct? If not, what is the first step?). If so, I'm having ...
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1answer
280 views

SVD and how to get two points on a 3D line from the representation of the line by means of two intersecting planes?

I have a 3D line represented by the intersection of these two planes $a_1x+b_1y+c_1z+d_1=0$ $a_2x+b_2y+c_2z+d_2=0$ I need to compute two 3D points $P_1=(x_1,y_1,z_1)$ and $P_2=(x_2,y_2,z_2)$ ...
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1answer
81 views

Evaluating the similarity of watermarks

I am working on an assignment where we have to use the NEC algorithm for inserting and extracting a watermark from an image file. Using the techniques described in this article. I am at the point ...
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1answer
214 views

How to use a graph cut

I have to use a graph cut to create a binary image from a grayscale image. I can easily compute both energy functions $E_{data}$ and $E_{smooth}$. But after that, I don't know what is the next step. ...
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1answer
259 views

Determining camera orientation (possibly using calibration images).

I need to generate a camera calibration pattern. Cameras are expected to be placed at an average height of 15 to 30 feet above ground pointing downwards at roughly 30 degrees. These cameras are ...
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1answer
80 views

Limiting search space for efficient line matching [closed]

I have 2D line segments extracted from an image. So i know end point coordinates of them. also, i have some reference 2d line segments. Both line segments are now in vector form. comparing to ...
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1answer
47 views

SVT algorithm and the value of tau.

SVT stands for singular value thresholding. It is an algorithm used in "matrix completion" problems. see http://svt.stanford.edu/ for basics. What is the meaning of "for large values of [tau]..." ...
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63 views

Limiting search space around line segment via rectangular buffer

I have 2D line segments extracted from an image. So i know end point coordinates of them. also, i have some reference 2d line segments. Both line segments are now in vector form. comparing to ...
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100 views

Can a matrix based “secret sharing scheme” be applied to image based secret sharing?

I was reading this and was wondering if it can be used to do secret sharing with images. I dont know a lot about image processing, but if the authors have given a scheme for matrices, how can be ...
3
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1answer
118 views

Solving ill posed linear equations

Given a set of linear equations $AX=B$, say $A$ is an ill posed matrix (has a few singular values equal or very close to zero), which numerical algorithm (conjugate gradient, least squares or steepest ...
3
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1answer
2k views

Explanation of this image warping (bulge filter) algorithm

I've been researching image warping algorithms lately and haven't found many comprehensive references. That said, there are of course code snippets from GIMP, jhlabs.com, and imagemagick.org but none ...
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0answers
109 views

2-D DFT of a matrix PxP and 1-D DFT of a vector of size P^2?

What is the difference between the following two things: make a 2-D Discrete Fourier Transform of a certain matrix A[p,p], first reshape this matrix into a 1-D vector a[p^2,1], and compute the 1-D ...
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188 views

Maximum absolute deviation

Let be I , J a two gray scale image How I will be able to interpret the Maximum absolute deviation between the histograms of these images?
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0answers
223 views

Lloyd-Max Quantizer Problem

Consider the function $z = x^2 + y^2$ , for $0 \leq x \leq 10$ and $0 \leq y \leq 10$. Take a regular discretization with steps $\Delta x = \Delta y = 0.1$ and its histogram as the probability ...
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1answer
36 views

Quantization Uniform

Let the output of image sensor take values between 0 to 10. If the samples are quantized uniformly to 256 levels, show that transition and reconstruction levels are $$t_k=\dfrac{10(k-1)}{256},\, ...
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1answer
111 views

Iterative model fitting

I have a sequence of points $\{(x_k,y_k,z_k)\}$ and I need to fit some $2D$ model $P(x,y)$ that approximates $z$ in some sense. The $z_k$$'s$ are noisy samples of some $2D$ function $z_k = f(x,y) + ...
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213 views

Calculating the aspect ratio of the rotated rectangle on the image

I need to determine the aspect ratio of the rectangular object (such as mobile phone or credit card) on the image. The problem is that the object might be photographed from an angle or perspective. So ...
2
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1answer
119 views

Gradient of the image

I'm trying to make a gradient flow for an image. For a test I made a small image 3x3 pixels with a black pixel in the middle. I found how to compute the direction of the gradient for one point given ...
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0answers
318 views

image classification problem using Matlab?

I have an image classification problem. I have an image which spesify classes' labels using "imread" funtion of Matlab $(A=imread('r.bmp'))$ the output for example for 3 classes is as $$A= ...
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1answer
67 views

Mean Square Error

I am ready the 101 page of the book [1], and I have a doubt. How I will be able to say: If $\sigma=\sum_{i=1}^{L}\int_{t_i}^{t_{i+1}}(u-r_i)^2p(u)du=0$; where $u$ is a scalar random variable with ...