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Questions tagged [image-processing]

This tag is for the mathematics involved in the field of image processing. Many such questions are also appropriate for Signal Processing Stack Exchange.

52
votes
2answers
16k 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 ?
3
votes
2answers
3k views

Back-projecting Pixel to 3D Rays in World Coordinates using PseudoInverse Method

For perspective projection with given camera matrices and rotation and translation we can compute the 2D pixel coordinate of a 3D point. using the projection matrix, $$ P = K [R | t] $$ where $K$ ...
2
votes
1answer
56 views

Why is finding $M$ eigenvectors on smaller matrix valid?

I am following this article on face recognition. In "calculating eigenfaces" section, the authors present a solution for the problem of calculating a very big matrix: Let $A_{N^2\times M}$ be an $M$ ...
5
votes
1answer
115 views

A property of the x-ray transform

Problem: Let $P_{\theta}f(x) = \int_{\mathbb{R}}f(x + s \theta) ds$ be defined as the x-ray transform, where $\theta \in S^{n-1}$, and $x$ belongs to $\Theta^{\perp}$, the hyperplane that passes ...
4
votes
0answers
664 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 ...
4
votes
1answer
640 views

Texture mapping from a camera image (knowing the camera pose)

I'm not sure if I should ask this question here or on stackoverflow, so forgive me if I'm wrong. I want to apply a texture (taken from a camera) on a 3D surface, let me explain my problem: I have ...
2
votes
1answer
162 views

Matrix values increasing after SVD, singular value decomposition

I am trying to learn SVD for image processing... like compression. My approach: get image as BufferedImage using ImageIO... get RGB values and use them to get the equivalent grayscale value (which ...
5
votes
4answers
5k views

PCA - Image compression

I have 2 questions related to principal component analysis: The first is, how do you prove that the principal components matrix forms a orthonormal basis? Are the eigenvalues always orthogonal? The ...
3
votes
2answers
112 views

Largest four line segments of polygon

I have some polygon (see darkblue contour): It consists of very small segments, pixel by pixel, so angles differ although they seem to be the same. Visually we see 4 large line segments. How can I ...
3
votes
5answers
914 views

How do I find/predict the center of a circle while only seeing the outer edge?

Question What formula would allow me to predict the center of this circle? In addition, what attributes of this image must be detected in order to predict the center? I figured understanding the ...
2
votes
0answers
291 views

Derivative of an Euclidean-Vector norm.

Consider: x a $N \times 1$ vector , with elements $x_i$ b a $N \times 1$ vector , with elements $b_i$ A a $M \times N$ matrix , with elements $a_{ij}$ ( Symmetric matrix - Block Circulant ) As we ...
2
votes
1answer
206 views

Minimum matching convolution

Let $\text{SPD}^n$ and $\text{PD}^n$ be the symmetric semi-positive and positive definite matrices in $\mathbb{R}^{n\times n}$, respectively. I want to find an $X\in \textrm{SPD}^n$ that minimizes $||...
1
vote
1answer
684 views

Convex Sets Pre-image

I am struggling with the following question: Let $a \in \mathbb{R}^n $ and $ b \in \mathbb{R}$ and define $ f: \mathbb{R}^n \rightarrow$ $\mathbb{R} $ by $f(x)=\langle x, a \rangle + b,x \in \...
1
vote
2answers
496 views

How do I compute the solid angle of a square in space in spherical coordinates?

I am trying to find out how to calculate a solid angle of a square or a rectangle in space, in a situation where we know θ and ϕ, being θ the polar angle and ϕ the azimutal angle the sphere has ...
1
vote
1answer
41 views

The image function in Mumford-Shah functional in image segmentation

My problem is about understandig (of physical interpretation) of image function $g$ in the Mumford-Shah functional. Let $\Omega \subset \mathbb R^2$ be an open domain, and $g \in L^\infty (\Omega)$...
1
vote
1answer
53 views

Boundary conditions in minimizing Dirichlet energy for an image processing problem.

Suppose $$\mathcal{L} =\mathcal{L}(x,y,u,u_x,u_y) = \frac{1}{2} \lVert \nabla u \rVert^2$$ and I want to find $u$ such that the functional $$ E(u)=\int_{\Omega} \mathcal{L}dxdy $$ is minimized, ...
1
vote
0answers
68 views

Given function $f$ find directional derivative of $\lVert \nabla f \rVert$ in direction given by $\nabla f$

Suppose we have a function $f(x,y)$ differentiable as many times as you like in $\mathbb{R}^2$ the gradient is given by $$ \nabla f (x,y) = \left(f_x,f_y \right)^T $$ cosine and sine of such vector ...
-1
votes
1answer
2k views

Calculate real length of object from perspective image- width of building [duplicate]

Please refer to the following image: I have the real height of the building which is $12.5 \text{ m}$ (red line). I have the blue lines in the image (pixels) as well as the red line. I have the ...