# 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.

18 questions
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 ?
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 $K$ ...
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 $M$ ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
206 views

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 ...
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 $g \in L^\infty (\Omega)$...
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, ...
### 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 ...
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 ...