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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 (and a slightly different objective function). Think of your image as graph $G$ with a node for each pixel in the image. There is an edge $(i,j)$ between two ...


8

I've implemented this recently, basically it counts how many times each specific colour borders another colour to make up a frequency table. To generate an image, a random colour and position are selected and the rest of the image is built up from there. Results aren't very coherent, but they match the colour palette of the original. In order to make sure ...


7

To add to Dmitry's answer (copied over from the deleted version of this question): Matrix-free finite elements are relatively well-known. For explicit methods for transient problems, this involves applying the finite element matrix using small reference matrices and geometry-specific transformations. For implicit problems, this is usually done in ...


6

Matrix-free method is a general name for a class of algorithms, rather than a particular method. For example, consider solving the linear equation $Ax=b.$ If you were to solve this this problem using the Gauss elimination method, for example, then you need to pre-compute all elements of $A$ and keep them during the algorithm. If you were to use Krylov-type ...


5

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 improvement. Additionally, once upon a time, the authors provided a code. I also tried it on my own dataset. Again, didn't work. Therefore, I am now sure that this ...


5

The gist of this answer is that this problem fits into a general framework that is part of machine learning. I think this can be done using the standard machinery of clustering / filtering problems in statistics, which are pretty standard. There's a lot of literature on this, so I'm going to present just the basic outline of how this can be done: it's easy ...


3

I will summarize a couple of possibilities: As a baseline, I would begin with a Hough transform kind of approach: Iterative Hough Transform for Line Detection in 3D Point Clouds Christoph Dalitz, Tilman Schramke, Manuel Jeltsch There is also an online demo as well as source code. Here is another paper of the same Hough-approach: Hough Parameter ...


3

I think I can address the second part of your Question. The phrase "sum-normalized to zero" is a fancy way of saying "subtract the mean (average)", i.e. subtract the constant needed to give a zero sum over the resulting function (filter) values. The phrase "square-normalized to 1" applies to the result of the first phrase and means dividing by a (...


2

The images described in the paper are not independent, but are uniquely defined by a lighting direction which is 3 dimensional. You could thus construct any conceivable image (in this model) by lighting the scene from 3 orthogonal directions (x, y and z for instance). This corresponds to the rank being 3. Hope this helps.


2

IntraFace has an expression detector built in. However, if you would like to do a custom smile detector, then what you should do is to convert your spatial facial fiducial points to some kind of a feature vector, which could be input to a non-linear classifier such as SVM or MLP. A trivial way to do this would be to use angular relations (if the face is ...


2

The Eigenface algorithm transforms image patches (e.g. logo of beer) into a common data space where nearest neighbor search is performed for classification. In order to use Eigenfaces, you will need a training data set to compute the common data space. Therefore it requires some time to define a proper training set. Once you have a proper training set, I ...


2

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 $\alpha$. This is true for the Radon transform, as one easily verifies. Whether compressed sensing can be applied to it is something beyond my realm of knowledge.


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Just some quick ideas from someone who works in the realm of feature extraction in physical systems modeling such as this: you want to find the simplest and strongest differentiating characteristics of the different behaviors you're interested in classifying. First, though: do you know in advance the full extent of behaviors you wish to classify? If not, ...


2

3D local feature descriptors for shapes are very well studied. Typically, people tend to represent the input as a set of points (point clouds) and try to characterize the local neighborhoods with lower dimensional signatures a.k.a. descriptors. The traditional descriptors, analogous to their 2D counterparts, involve some kind of histogram-ing such as SHOT, ...


2

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, we can write $ \begin{align} b &= h*x\\ &=x*h \end{align} $ So we can have two equal representations using the matrices $H$ and $X$ corresponding to ...


2

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 create a correspondence between real and virtual spaces, ARKit uses a technique called visual-inertial odometry. This process combines information from the iOS ...


2

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 on the choice of algorithm and you have to be careful to make sure that $a$ and $b$ are always positive (by adding constraints). One way of approaching the ...


1

When the points belong to more than one curve, it will first be necessary to cluster them into curves. A possible approach is described together with a reference implementation in Dalitz, Wilberg, Aymans: TriplClust: An Algorithm for Curve Detection in 3D Point Clouds. IPOL 2019.234 (2019) When your points have an implicit parameter representing an ...


1

I think your problem can be written as an optimization problem. $\{x_i\}$ is the set of points for plane 1, $\{x_j\}$ for plane 2 respectively. Their orthonormal vectors are $n_1$ and $n_2$ with constraints: $|n_1|=1$, $|n_2|=1$ and $n_1n_2=0$. $\{\lambda_i\}$ the set of lagrange multiplier. The functional under constraints reads $$ \sum_i (x_i n_1-c_1)^2 +...


1

Here I devise a novel strategy, based on only 3D points, that I think, would work. I will parametrize a 3D plane by a point $\mathbf{p}$ and its normal $\mathbf{n}$. Imaging you take a pair of oriented points $\mathbf{p}_1$ and $\mathbf{p}_2$, on the point cloud $\mathbf{P}$ with corresponding normals $\mathbf{n}_1$ and $\mathbf{n}_2$. Let $\mathbf{d}$ ...


1

Software could never get rid of all the effects of distortion. The reason is that, if you do not operate in the hardware level, you could only make approximations about the real effects. Distortion models such as pin-cushion, barrel and etc are only the effects which we could model. The distortion removal techniques, which are based on some kind of ...


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Blog post on an experimentation using Markov to recreate art: https://magenta.as/using-machine-learning-to-make-art-84df7d3bb911 Code is on github made by @william-index: https://github.com/william-index/markov-fun


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If I understand correctly, the form of your problem seems similar to the one faced by a radar or sonar system. In that case, the sensor periodically outputs a number of "hits" or detections, each consisting of a time and a location in space. Machine learning brings powerful general methods to bear on problems of this form (as observed in the answer by ...


1

This OpenCV documentation page suggests that the Eigenfaces algorithm is simply dimensionality reduction using PCA and classification by nearest neighbor search. Fisherfaces uses Linear Discriminant Analysis instead, which aims to maximize between-class variance while minimizing within-class variance, and so may perform better in some cases. Neither of these ...


1

Please check this link: http://en.wikipedia.org/wiki/Precision_and_recall Check the ROC section as well. This is a very clear description I think. For a more thorough understanding, I would recommend: http://machinelearning.wustl.edu/mlpapers/paper_files/icml2006_DavisG06.pdf


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Take a look at this example showing how to detect objects in cluttered scenes in matlab. This should work well for finding a picture in a video. I am not sure I understand what you mean by "without playing the video". This can be done without you having to look at the video yourself, but your program would still have to read the video file frame by frame, ...


1

Have a look at OpenCV. It includes motion analysis and tracking, so depending on how complicated your setup is, it might be as simple as taking one of the sample programs, using it to compute the ball's motion and then looking for sharp changes in direction.


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I think you should take a look at "Eulerian Video Magnification", a method for magnifying imperceptibly small motions in a video that was invented by the CSAIL lab at MIT. In the process of doing this, they use a variety of signal processing techniques that may be useful to you. By using this technique, the researchers have been able to extract things like ...


1

To convert from Rodrigues vector to a rotation matrix (and back) please check the MATLAB code here: http://www.cs.ucla.edu/~soatto/vision/courses/268/rodrigues.m So this gives you the rotation matrix. You use the translation parameters directly. Additionally, you might want to form the camera matrix. It would be a good idea to get a fully calibrated K (...


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