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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2
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0answers
126 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 ...
0
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0answers
361 views

Maximum absolute deviation

Let $I$, $J$ be two gray scale images. How will I be able to interpret the maximum absolute deviation between the histograms of these images?
2
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0answers
415 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
votes
1answer
52 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},\, k=1,...
3
votes
1answer
155 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) + n(...
1
vote
0answers
346 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
141 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 ...
1
vote
0answers
408 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= \begin{...
0
votes
1answer
74 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 ...
1
vote
2answers
444 views

Unitary Matrix for Image Processing

Why usually consider unitary matrices to define image transforms?
1
vote
1answer
292 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 ...
6
votes
1answer
859 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 ...
1
vote
0answers
350 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
votes
1answer
35 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
votes
1answer
315 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
votes
1answer
100 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
votes
1answer
73 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
vote
3answers
158 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. ...
4
votes
5answers
1k 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 ...
2
votes
1answer
648 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
92 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
votes
1answer
726 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
votes
0answers
390 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 ...
2
votes
0answers
87 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.
3
votes
0answers
5k views

About Sum of Squared differences

I found a paragraph in the book about $SSD$, can't get one thing: Most commonly, the distance measure is the sum of squared differences. For two images $f(x, y)$ and $g (x, y)$ it is defined as ...
0
votes
1answer
443 views

How do I handle image gradient calculation at the edge of images?

The image gradient is the rate of change over any given pixel of an image, either in the horizontal or vertical direction. An image can be thought of as a large matrix of values [0, 255]. A common ...
1
vote
1answer
1k views

Two Quadrilaterals Intersection Area (Special Case)

I have two intersecting quadrilaterals (the area of intersection is the grey polygon with thick boundary): These properties holds: One quadrilateral is always a rectangle There is always some ...
0
votes
2answers
4k views

DFT and DWT difference?

what is the basic difference between the Discrete Fourier Transform and the Wavelet Transform ? and why does JPEG2000 preferred DWT over DCT or DFT ?
6
votes
4answers
3k views

Laplacian 2D kernel - is it separable?

I'm wondering if the 2D laplacian kernel 0 1 0 1 -4 1 0 1 0 is also a separable kernel. How can I find that out?
0
votes
2answers
199 views

How to solve this 2-D deconvolution $g*f=δ$?

$g*f=δ$, where $*$ refers to convolution, $δ$ is impulse, $f$ and $g$ is 2-D matrix, $f$ is given and sum of all the elements in $f$ equals $0$, $g$ is unknown. i want to find $g$. i would appreciate ...
2
votes
1answer
338 views

Is it valid to compose affine and perspective transformation matrices?

According to image processing literature, it is valid to compose multiple affine transformation matrices in order to apply just one transformation matrix to an image instead of subsequently applying ...
0
votes
1answer
460 views

Applying a transformation matrix to a matrix of larger dimension, like a grey scale image

I have a new job in image processing and just earned my BS in Physics. I know enough to make a lot of mistakes... I have been reviewing my linear algebra a lot lately, especially the affine ...
0
votes
1answer
721 views

Finding radius r of the overlappable sphere(s) in 3D image

My current problem: I have an input 3D binary image (a 3D matrix that has only 0 and 1) that consists of random numbers of sphere with radius r. We do not know how many spheres are there in the ...
12
votes
3answers
17k views

What does the Fourier Transform mean in the context of images?

This is clearly a very important equation with tonnes of properties that I see come up a lot in image processing literature, but I don't understand why this equation is important, and what it is ...
1
vote
1answer
11k views

What does it mean to divide by the standard deviation?

I'm trying to variance normalise an image, in order to do so, I subtract the mean from the pixel value, to have a 0 mean, and divide by the standard deviation, to have a unit variance, right ? but I'...
0
votes
1answer
719 views

Explanation of sinusoidal function: $f(x,y) = A\cos(2\pi(ux + vy) + \phi)$

I never got to take a signals and systems course and this has come up in the math of my image processing review. Can this be explained? The equation for a sinusoidal signal is $f(x,y) = A\cos(2\pi(...
0
votes
1answer
807 views

Could explain me how eigenvector helps with compute gradient and how make differentiate operation on decrete space like digital image?

Could you explain me how eigenvector helps with compute gradient and how make differentiate operation on descrete space like digital image? I know that this question is so connected with computer ...
37
votes
2answers
9k views

What do eigenvalues have to do with pictures?

I am trying to write a program that will perform OCR on a mobile phone, and I recently encountered this article : Can someone explain this to me ?
2
votes
0answers
191 views

Singular Value Decomposition

I want to decompose an image $A$ using the Discrete Wavelet Transform and then find the singular values, $S$, such that $A=USV$. I will then do the same to another image such that $B=USV$. I will ...
1
vote
1answer
109 views

Taking a derivative of this formula

I reading an article about an Automatic scale selection It is used in image feature extraction. But what I need is the mathematical part of it. I have a problem with understanding the following: ...
2
votes
0answers
87 views

Intuition about moment function derivation [OR] derivatives involving a time varying integration domain

$$ m_{{pq}}(t)=\iint\limits_{R(t)}h(x,y) dx dy $$ where $ R(t)$ the domain of integration is time varying (In fact it is the only one which is time varying). And $$ h(x,y) = x^p y^q f(x,y) dx dy ...
44
votes
2answers
7k views

Mathematical explanation behind a picture posted (lifted from facebook)

In this image given below, there is an actor's (famous south Indian actor Rajinikanth) image which can be seen only if you shake your head ! I had lifted this from Facebook. I am just curious to ...
4
votes
1answer
937 views

Unscramble images without trying all permutations

I try to write an algorithm that unscrambles images that were before scrambled by mixing up small blocks: My idea is that in the bottom image there are more "sharp" corners compared to the image ...
3
votes
2answers
121 views

How can I measure the properties of a Point Spread Function?

What quantity or property can I use that describes by how much a point spread function distorts/blurs an image?
1
vote
1answer
344 views

Identifying 3D shape from matrices analytically

I have a set of matrices (a 3D matrix, that represents a quantized body), for instance: (the size 5x5 here is just an example, the real size is a lot higher) $ M_1 = \left[ {\begin{array}{cc} 0 &...
1
vote
2answers
292 views

What is an efficient way to get blur from source and blurred images?

I'm doing little program to get blur from source image and blurred image. But I haven't learned so much things about math in school yet. The equation used for blurring the image A into B: ...
1
vote
1answer
159 views

Reconstructing a ring from a stack of 2D images (radially aligned)

I have a stack of images (about 180 of them) and there are 2 black dots on every single image. Hence, the position(x,y) of the two stars are provided initially. The dimensions of all these images are ...
1
vote
1answer
82 views

A function for forming a closing curve on all points on a 2D image

First of all, this is for image processing. The small circles above is on an image and are my list of points. The points are always in order from p1, p2, p3 to pn. And I am to create a curve that must ...
1
vote
2answers
371 views

Scaling a histogram in the face of outliers

I am trying to figure out how to display a histogram of a digital image in the face of massive outliers (lots of shadows, highlights, or lots of anything inbetween). If I simply choose the bin with ...
8
votes
1answer
224 views

Homotopy and watershed

homotopy is a new word to me. Upon trying to understand this property, I immediately think of another well-known segmentation algorithm: watersheds. I see that watershed should exhibit some ...