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Well, look at your original picture: it's constant for all points but the edges, which means your derivative is zero for all points but these edges. By applying a "rounding, smoothing" filter to it, you "smear" the edges enough to make the derivative be non-zero for multiple pixels, in every direction.


2

That is because correlation (and convolution) are not meant to "match" exactly a given pattern. They are multiplicative operators in their nature so they are strongly related to signal amplitude if you multiply the reference signal by N, the output gets twice bigger. for instance your operator will return a peak twice higher when encountering this piece of ...


2

As it was already posted multiple times: The problem comes from an inaccurate definition of correlation in your application. The Pearson correlation coefficient does require the data to be centered, ie the mean must be subtracted normalized, ie the data must be divided by the standard deviation This centering and normalization must be done for the mask ...


2

You picked a tough example. Short answer: Change your "0"s to another value, e.g., 2, and it should work much better. What's really happening: your signals are not zero mean, correlation requires to center the signals (i.e., subtract means). Example, since it's easer to understand in 1-D: say you want to find the pattern p=[0,2,2,0] in the sequence s=[2,...


2

This might be hard with trying to illustrate this way but here I go. Take your original image and put the filter in the upper left corner like so: +-------+-------+---+---+ | 1 [0] | 1 [0] | 1 | 1 | +-------+-------+---+---+ | 1 [1] | 1 [1] | 1 | 1 | +-------+-------+---+---+ | 0 | 0 | 1 | 1 | +-------+-------+---+---+ | 1 | 1 | 1 | 1 | +----...


2

The term image derive from Latin imago. I fully agree with wikipedia saying that it denotes an artifact that depicts visual perception [...] that resembles a subject—usually a physical object—and thus provides a depiction of it. As such, it is a representation of some reality, combining spatial "ordinal" cooordinates (with some natural order, in 2D ...


2

A simple way to calculate contrast is by computing the standard deviation of the greyed image pixel intensities.


1

Some references on image sharpness metrics: Encoding Visual Sensitivity by MaxPol Convolution Filters for Image Sharpness Assessment, IEEE Transactions on Image Processing, 2019 A Fast Approach for No-Reference Image Sharpness Assessment Based on Maximum Local Variation, IEEE Signal Processing Letters, 2014 Image Sharpness Assessment Based on Local Phase ...


1

I wrote a function which solves this in my StackOverflow Q2080835 GitHub Repository (Have a look at CreateImageConvMtx()). Actually the function can support any convolution shape you'd like - full, same and valid. The code is as following: function [ mK ] = CreateImageConvMtx( mH, numRows, numCols, convShape ) CONVOLUTION_SHAPE_FULL = 1; ...


1

filtfilt() is a technique to achieve zero-phase filtering by applying the same filter twice to the data; with the output of the first stage reversed and filtered again in the second stage. Zero phase filtering is a desired property in image processing. NaN means "not a number" and indicates those indeterminate conditions like $0/0$, $\infty/\infty$, $\infty ...


1

What I resorted to was using the pypi package, which is advertised here: http://www.cs.tut.fi/~foi/GCF-BM3D/index.html#ref_software . I digged a bit in the source code, and found that I could perform BM3D, in the following fashion: import bm3d denoised_image = bm3d.bm3d(image_noisy + 0.5, sigma_psd=30/255, stage_arg=bm3d.BM3DStages.HARD_THRESHOLDING) I ...


1

Looking at Intel - An Investigation of Fast Real Time GPU Based Image Blur Algorithms By Filip Strugar it looks like the Kawase kernel is just a way of implementing a linear kernel quickly, but in a way that constrains the kernel somewhat. This means that you could make such an algorithm. Either choose a set of spreads and adjust their weights (if that is ...


1

Taking a step back, a standard image $I$ is composed of pixels. They are defined by a location (spatial coordinates, here denoted by $p$), and a "value", denoted by $I_p$. Smoothing or enhancing an image, in a large sense, consists in replacing each $I_p$ by $\hat{I}_p$, a value that would be: more probable, more consistent, more visually pleasant (choose ...


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I would start with the many resources on this site: Is the Bilateral Filter a Solution of Some Variational Method? How to Validate Bilateral Filter Implementation? Comparison Between Guided Filter (Edge Preserving Filter) and Gaussian Filter. What Is the Bilateral Filter Category: LPF, HPF, BPF or BSF? Understanding the Parameters of the Bilateral Filter. ...


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I would rephrase your terms as: the "directional derivatives" are not so directional (although sometimes called similarly in lecture, they are only horizontal and vertical. Truer "directional derivatives" would allow angular refinement, cf. non-separable filters (Deformable Kernels for Early Vision, Perona) the "directional derivatives" are not so ...


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