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

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1answer
101 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 ...
-1
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1answer
139 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: ...
0
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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
82 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
116 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: ...
2
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2answers
767 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
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 ...
2
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1answer
104 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
166 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
votes
1answer
222 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
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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 ...
0
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1answer
74 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 ...
1
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1answer
359 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
274 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 $P_2=(x_2,y_2,z_2)$ ...
1
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1answer
76 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 ...
1
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1answer
206 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. ...
1
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1answer
241 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
78 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
vote
1answer
46 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
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 ...
0
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0answers
98 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
114 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
1k 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
103 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
185 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?
2
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0answers
207 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 ...
0
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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},\, ...
3
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1answer
109 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
197 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
votes
1answer
116 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
305 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
62 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
207 views

Unitary Matrix for Image Processing

Why usually consider unitary matrices to define image transforms?
1
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1answer
125 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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0answers
268 views

Distance between two objects in a picture

lets say I have a photo that has a picture on a wall and a book upright on the desk. now i know the size of both of these objects. I want to find the distance between two of them on the photo, I was ...
6
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1answer
602 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
203 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 ...
0
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1answer
33 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 ...
0
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1answer
212 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 ...
0
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1answer
86 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 ...
0
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1answer
65 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 ...
1
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3answers
112 views

How do I find a number that will scale an image but keep the dimensions whole numbers

I have an image with width 4096 and height 2896. I would like to scale the image to below 4000 pixels wide - and as close to 4000 as possible. I would also like to keep the dimensions whole numbers. ...
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5answers
805 views

The mathematics behind Fourier Transform for Image Processing

I am following http://homepages.inf.ed.ac.uk/rbf/HIPR2/fourier.htm . I understand the application of Fourier Transform behind Image Processing, but right now, I am curious about the mathematics behind ...
1
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1answer
303 views

Normalizing 2D coordinates that are arbitrarily transformed.

This was originally posted as a programming question so I will try to keep it as abstract as possible. We are dealing with two images. The first is the original and second is a distorted version of ...
0
votes
1answer
87 views

Create a new image from an image set's patterns

So, I'm interested in learning how to detect patterns in a set of images and then use those patterns to create a new image of similar style. For example, say there is a group of 20~ish images ...
4
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1answer
298 views

How to resize an image?

I am not sure about the title of this question, so if someone knows an appropriate one, please rename it. It's a programming related question (but doesn't involve any programming). I posted it on ...
4
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0answers
241 views

Reprojecting/converting an orthographic image/grid into a cartesian grid

I'm trying to dewarp a fisheye image into a simple rectilinear image of a subset of the fisheye. As part of this, I'm trying to map the azimuth/altitude values into a point on the image. The points ...
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0answers
65 views

Principal Component Analysis software

I'm looking for a (non-MATLAB) software that can process a image using the PCA algorithm and output it like this: Regards.
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0answers
337 views

Circular to linear convolution with matrices

I know how to perform a circular convolution with vectors (http://engineering-matlab.blogspot.it/2010/12/matlab-program-for-implementing_5864.html) and I know that circular convolution can be obtained ...