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If I understand your method 1 correctly, with it, if you used a circularly symmetrical region and did the rotation about the center of the region, you would eliminate the region's dependency on the rotation angle and get a more fair comparison by the merit function between different rotation angles. I will suggest a method that is essentially equivalent to ...


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Common Approaches for Commercial Denoisers Commercial denoisers are different than what you'd see on most papers. While on papers the results are mostly using objective metrics (PSNR / SSIM) and are evaluated vs. Additive White Gaussian Noise (AWGN) with high level of noise real world images are mostly with moderate level of noise with Mixed Poisson ...


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There is a similar DSP trick here, but I don't remember the details exactly. I read about it somewhere, some while ago. It has to do with figuring out fabric pattern matches regardless of the orientation. So you may want to research on that. Grab a circle sample. Do sums along spokes of the circle to get a circumference profile. Then they did a DFT on ...


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Digital image processing is an extension of digital signal processing and linear system theory into two dimensional signals. Image processing involves all low level tasks such as filter design and filtering, spatial scaling, sampling, intensity manipulations, geometry manipulations, Fourier analysis and spectrum analysis, motion estimation, noise reduction, ...


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The result of a convolution of a data vector of length M with a kernel of length G is of length M + G - 1. (the maximum length of the non-zero portion, even though the limits of integration is sometimes written as from -infinity to +infinity) This is clearly (G - 1) elements longer than the original data vector. So where do these new, "extra", additional ...


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I've went ahead and basically adjusted the Hough transform example of opencv to your use case. The idea is nice, but since your image already has plenty of edges due to its edgy nature, the edge detection shouldn't have much benefit. So, what I did above said example was Omit the edge detection decompose your input image into color channels and process ...


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This is a go at the first suggested extension of my previous answer. Ideal circularly symmetric band-limiting filters We construct an orthogonal bank of four filters bandlimited to inside a circle of radius $\omega_c$ on the frequency plane. The impulse responses of these filters can be linearly combined to form directional edge detection kernels. An ...


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Approximation by the real part of a weighted sum of separable complex Gaussian component kernels Figure 1. The proposed scheme illustrated as 1-d real convolutions ($*$) and additions ($+$), for cut-off frequency $\omega_c = \pi/4$ and kernel width $N=41$. Each the upper and the lower half of the diagram is equivalent to taking the real part of a 1-d ...


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I myself recently graduated from Applied Mathematics and began PhD in signal processing. I do Stochastic Geometry modeling of wireless networks in particular, which is quite mathematical subject. It involves measure theory, probability theory, Fourier Analysis etc. etc. The area of Signal Processing is very broad indeed. It of course depends if you want to ...


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In general, the time derivative property of the Fourier Transform is given as $$\mathscr{F}[\frac{d}{dt}x(t)] = j\omega X(j\omega) $$ Notice that we can simply multiply by the frequency index in the Fourier Transform result. For the 2D FT result: $$\mathscr{F}[f(x,y)]= F(u,v)$$ Using the same property results in: $$\mathscr{F}[\frac{d}{dx}f(x,y)]= uF(u,...


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Sampling is the process of making the x-axis (time) discrete and quantization is the process of making the y-axis (magnitude) discrete. You can sample without quantization (such as done with an analog sample and hold circuit). Quantization is introduced through rounding or truncation when the sampled analog signal is mapped to a digital representation. ...


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In my StackExchange Signal Processing Q38542 GitHub Repository you will be able to see a code which implements 2D Circular Convolution both in Spatial and Frequency Domain. Pay attention to the function CircularExtension2D(). This function align the axis origin between the image and the kernel before working in the Frequency Domain. Remember that for ...


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We need to assume the reader knows some basic stuff to answer that. Let's give it a try. Lets understand the sentence - Zero / First Order Hold. We have the Zero / First Order and the Hold. Zero / First Order hold means the order of the Taylor Series of the function we use to interpolate. In other words, the degree of the Polynomial we can write the ...


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Why Does 2D FFT of Gaussian Looks More Sharper than Gaussian Itself? Have a look at the Fourier Transfrom of a Gaussian Signal. $$ \mathcal{F}_{x} \left\{ {e}^{-a {x}^{2} } \right\} \left( \omega \right) = \sqrt{\frac{\pi}{a}} {e}^{- {\pi}^{2} \frac{ {\omega}^{2} }{a} } $$ First, Gaussian Signal stays Gaussian under Fourier Transform. As you can see, the ...


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This is a good question and something that I remember asking myself when I first learned about impulse responses and convolution. To understand this, it is first necessary to understand the significance of impulses and impulse responses. Referring to the image below, you can see that an impulse is an instantaneous like input and the impulse response is the ...


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In the Total Variation framework we define 2 flavors: $$ \text{Isotropic TV} \; {TV}_{ {L}_{2} } \left( X \right) = \sum_{ij} \sqrt{ { \left( {D}_{h} X \right) }_{ij}^{2} + { \left( {D}_{v} X \right) }_{ij}^{2} } $$ $$ \text{Anisotropic TV} \; {TV}_{ {L}_{1} } \left( X \right) = \sum_{ij} \sqrt{ { \left( {D}_{h} X \right) }_{ij}^{2} } + \sqrt{{ \left( {D}_{...


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Focus on the first equation for EY. Back in the day when color television was being developed, the color signal had to be compatible with black and white TVs and vice versa. So the compatible brightness signal (luma Y) has to be calculated from the three primary color signals (R, G B) for transmission. Human visual system does not perceive brightnesses of ...


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Rather performance intensive, but should get you accuracy as wanted: Edge detect the image Hough transform to a space where you have enough pixels for the wanted accuracy. Because there are enough orthogonal lines; the image in the hough space will contain maxima lying on two lines. These are easily detectable and give you the desired angle.


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Excerpted from Jae S.Lim 2D signal and image processing ch.1, as an example of $2$-D circularly symmetric lowpass filter with a cutoff frequency of $\omega_c$ radians per sample, whose impulse response is given by: $$h[n_1,n_2] = \frac{\omega_c}{2\pi \sqrt{n_1^2 + n_2^2} } J_1 \big( \omega_c \sqrt{n_1^2 + n_2^2} \big) $$ where $J_1$ is the Bessel function ...


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In the context of image processing (and machine vision as well), blurring is an operation that reduces the sharpness of an image by some lowpass filtering applied on it. There are different causes of blurring such as lens blur, motion blur, or just LSI (linear shift invariant) lowpass filtering. Deblurring refers to any restoration performed on the image ...


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Let me present the following Diagram: So, both Deblurring and Deconvolution are operations within the family of Image Restoration (Which is a subset of Inverse Problem set). Basically we build the Image Restoration set by different Degradation Models. The one related to the question are: Linear Degradation Model Namely, the degradation is made by a Linear ...


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General Idea The general idea of Principal Component Analysis (PCA) is as following (Intuition over formalism): Given a set of points in space (Inner Product Space) find a set of vectors (Directions) which are uncorrelated which span the data in the most energy preserving manner. The tricky part is explaining "most energy preserving manner". So we're ...


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Answer to the first post I guess that is pretty much dependent on the problem that you are dealing with. Boundaries are always a problem that needs extra care. In most applications, it would be an option to set those values to zero (and handle normalization factors of the filter appropriately). Other options would be to reflect the data, so that the index ...


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Questioner's answer... sigma have the same units as x and y i.e. number of pixels. In multi-scale filtering, the size of the filter must change when the sigma changes. Obtain the number of pixels per one millimeter or the vice-versa. (I did this using the property of pixel spacing included in the DICOM metadata in Matlab you can do this as info=dicominfo('...


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In support of Comparable mixin, a default <=> or spaceship operator for pixels is defined in the function Pixel_spaceship in rmpixel.c. However, in your use of the sort method, you define your own code block that overrides the <=> operator, and yours takes a single argument rather than two which would be correct, so the definition is broken and ...


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Your interpretation is correct: directional derivation operators highlight variation in a given direction. Here, you use the $2$-point discrete derivative in the $x$-direction (along image rows). It may emphasize vertical features. First, such operators indeed extend the initial image range. However, one often uses the absolute value of the derivative to ...


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MATLAB is one of the most important software inventions of the twentieth century, from a DSP point of view its syntax is simply the best in the world. And image processing is one of its strongest parts. However it's mainly of academic focus and if you look for industrial output you should consider having a number of additional tools. LabView is one such ...


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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.


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