# Tag Info

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### Interpolation by Solving a Minimization Problem (Optimization)

This is the classic colorization using optimization problem. Optimization and Linear Algebra To see how this can be expressed as a linear system, it's helpful to use a slightly different notation (...

### How to separate text from the paper on a black and white page?

I believe the best approach here is to use a threshold based on the local average brightness of the image. Setting the threshold to be 90% of the mean value of the 11x11 grid surrounding each pixel ...

### discrete definitions of curl $\nabla \times F$?

Continuous It looks like you only need 2d curl, so let's start with a simpler continuous definition: $$\omega = \nabla \times \mathbf{u} = \frac{\delta v}{\delta x} - \frac{\delta u}{\delta y}$$ ...
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### Iterative camera calibration - No convergence

I have to tell you. I implemented this algorithm (even double checked with other experienced people), however no luck. I guess, this worked for the authors, but with our data there was really no ...

### Shape measure for C-shaped objects

How about something like radial integral channel features? Affordable person detection in omnidirectional cameras using radial integral channel features, Barış Evrim Demiröz, Albert Ali Salah, Yalin ...
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### Which image filter acts like "surface tension"?

Morphological Closing. A morphological closing is a combination of dilation followed by erosion; typical image processing operations available in most image processing libraries. SciPy has a "...

### Eigenvalue decomposition for a very huge matrix of medical images (such as the pixel physical coordinates of CT images)

Take a look at the literature that does similar things for facial recognition -- search for the term "eigenface", for example. The point to make in this context is that the information you ...

### Cloud solutions for microscopy image analysis

Awesome to find another microscopist on this site. Welcome! Short Answer: There is no magic-bullet on the market that will solve this problem space for you. Longer Answer: Putting together a few ...
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### Compare reconstruction of matrices using SVD

PSNR, the ratio between the peak power of the true signal and the power of the Gaussian noise, measures the amount of mathematical error introduced in an image by compression or noise introduction. ...

### Calculate the area and perimeter of a hand-drawn shape

Writing my comment idea in more detail: Lets say you have your image input to your application as a black and white pixel array, for example something like: Then each black pixel can be represented ...
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### Compute point-spread-function between original and blurred image

We construct an operator based on the assumption that the system is a linear space invariant system. The blurred image is denoted $b$ and the input is denoted $x$. Since the convolution is commutative,...

### Natural spline conditions for 2D cubic splines

There are two different ways to extent cubic splines to 2D. The more official approach is the tensor product approach. On the boundaries where $x$ is constant, you require $S_{xx}=0=S_{xxy}$. On the ...
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### What are the numerical methods for testing for dissimiliarity between image based probability histograms?

Sounds like a job for the Earth Mover's Distance (or Wasserstein metric). In computer science, the earth mover's distance (EMD) is a measure of the distance between two probability distributions. ...

### Fitting rectangle to segments in image

You might be able to do better than simple gradient descent using an algorithm like BFGS, which uses the history of the gradients as well as the approximate solutions to try and approximate the ...
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### What are the most popular wavelet or tight frame regularizers for image reconstruction problems?

EDIT: some code made available] From a personal experience, and in the work of colleagues, we observed that multi-band dual-tree wavelets, a type of low-redundancy oriented decompositions based on ...

### discrete definitions of curl $\nabla \times F$?

This is made a lot easier by introducing the Calculus of Finite Differences. If $u_{i,j}$ is grid function defined for integer $i,j$ then the y-differencing operator $$\delta_y u=u_{j+1}-u_j$$ is ...

### Open Source MRI Image Stacks

As I mentioned before, you can try with the Visible Human Project. You can also go with 3D Slicer sample data, e.g., the Knee Atlas or the Brain Atlas. Their terms are quite permissive: By ...

### Automatic motion recognition

You would greatly benefit from knowledge in signal processing, but some specific useful knowledge would be in computer vision and estimation (like Kalman filters or alpha beta filters). With respect ...

### Is the inverse radon transform considered a linear operation?

For an operator $R$ to be linear, it has to satisfy two conditions: $R(f+g) = Rf + Rg$ for any two operands $f,g$; $R(\alpha f) = \alpha Rf$ for any operand $f$ and (real or complex) number $\alpha$. ...
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### What is a good algorithm, and framework, to calculate centres of gravity or mass (cog)?

There are several alternatives: Alternative #1: you need to find for each cell of the tessellation the list of pixels contained in the cell. To do that, you can use a rasterization algorithm. You can ...

### Computational Complexity of 2D Convolution

You can optimize the convolution, using separable theorem. Let me give an example. Image ($M\times N$): 1024, 768 (Grayscale) Convolution mask ($k\times k$): 7x7 Computational complexity: ...

### Which technique to use for signal/image processing or noise removal?

You may start with median or Gaussian filters. There are many libraries that implement them and they are simple to use. That said, I think this approach may be not enough because from what I've seen ...

### Which image filter acts like "surface tension"?

I think that you could use a Gaussian Filter. The following Python code does something similar to what you show in your images. ...
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### Polygon approximation with a circle

They just curve fit the two equations $$x(\omega) = h - b \sin(\omega) ~,~~ y(\omega) = k + a \cos(\omega)$$ using a nonlinear curve fitting algorithm. However, the accuracy of the fit depends ...

### Is there an efficient algorithm for matching objects in one image to objects in another?

Disclaimer: This is most likely not the most efficient, promising way to go about it. When I was looking up the same topic from a similar interest (Analyzing microscopy images), I came across the ...

### Is there an efficient algorithm for matching objects in one image to objects in another?

I guess what you are referring to is the cross-correlation between the images. This is very good and efficient to find shifts, but not changes in scale and orientation. As you probably know, the cross-...

### Algorithm to determine flat surfaces and camera orientation without specialized hardware

You are quite right, Augmented Reality benefits a lot from a combination of video/image analysis together with the data from motion sensors. Quote from Apple ARKit: Understanding World Tracking: To ...