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

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2
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1answer
43 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
votes
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
vote
1answer
340 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
votes
1answer
269 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
vote
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
vote
1answer
205 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
vote
1answer
216 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 ...
-1
votes
1answer
77 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
45 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]..." ...
0
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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
votes
0answers
97 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
votes
1answer
112 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
votes
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 ...
2
votes
0answers
102 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
votes
0answers
183 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
205 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
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
votes
1answer
106 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) + ...
1
vote
0answers
192 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 ...
1
vote
1answer
108 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
302 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= ...
0
votes
1answer
59 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
194 views

Unitary Matrix for Image Processing

Why usually consider unitary matrices to define image transforms?
1
vote
1answer
124 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 ...
0
votes
0answers
267 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
votes
1answer
591 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
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0answers
199 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
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
votes
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
votes
1answer
85 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
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
vote
3answers
111 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
774 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
vote
1answer
289 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
votes
1answer
289 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
237 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
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0answers
64 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.
0
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0answers
335 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 ...
3
votes
0answers
3k 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
264 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
657 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
2k 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 ?
5
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3answers
1k 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
183 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
291 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
194 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
341 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 ...
11
votes
3answers
11k 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
4k 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 ...