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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3answers
392 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
377 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
83 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
859 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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2answers
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
687 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
95 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
216 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
148 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
159 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
250 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
49 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
33 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
248 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: ...
4
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2answers
1k 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 ...
4
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1answer
97 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 ...
2
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1answer
130 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
285 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 = ...
7
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1answer
269 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) ...
2
votes
1answer
48 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
87 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
671 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 ...
3
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1answer
321 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
119 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
272 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
347 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
83 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 ...
1
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1answer
59 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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0answers
70 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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0answers
109 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 ...
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1answer
138 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
120 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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0answers
234 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
301 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
39 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},\, ...
3
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1answer
138 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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0answers
267 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
129 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
371 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
70 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 ...
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2answers
306 views

Unitary Matrix for Image Processing

Why usually consider unitary matrices to define image transforms?
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1answer
176 views

What does it mean to convolve a matrix with a kernel?

I have a Matrix, M, of dimensions width x height. The problem is to apply the [-1, 0, 1] filter along the x and y axis (i.e. convolve the image with [-1, 0, 1] kernel along horizontal and vertical ...
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1answer
730 views

any idea what fractal algorithm might generate this shape?

I Found this image around, and i'm curious what algorithm generates this kind of shape In particular, i'm curious how the flow lines are generated, since usually the Mandelbrot iteration just ...
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0answers
252 views

Projection Slice theorem getting rid of artifacts?

I have employed the fourier(projection) slice theorem in matlab. I have a 3D image, P(x,y,z) defines their pixel intensities at a given location int he image volume, it is discrete and uniform. I ...
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1answer
34 views

Confusion related to an edge detection filter

I was reading this article related to edge detection and here is a edge detection mask -1 0 1 -1 0 1 -1 0 1 It's mentioned that this detector detects the edges ...
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1answer
256 views

Point spread function (PSF) expressed as a convolution and a sum

The Wikipedia article on the Point Spread Function (link) discusses how an imaging system can be conceptually described using linear system theory. A convolution of the PSF with the image in the ...
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1answer
93 views

recovery plane from 4 point imaging using calibration camera

I have a camera and its K matrix (calibration matrix) also I have image of plane, I know the real points of the 4 corners and thier correspondence pixel. I know how to compute the H matrix if z=0 (H ...
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1answer
69 views

Solving this image focal problem?

Suppose you wish to form an image of a 1cm wide object, 50cm away, on a sensor measuring 20mm. How can I calculate the magnification factor required and the focal length of the lens? I'm not sure how ...