4
Indeed you can do that.
You may look on my answer to How to Prove a 2D Filter Is Separable?
By the SVD for any filter $ A $:
$$ A = \sum_{i = 1}^{n} {\sigma}_{i} {u}_{i} {v}_{i}^{T} $$
Since we're talking about separable filter then:
$$ A = {\sigma}_{1} {u}_{1} {v}_{1}^{T} $$
So the columns filter is $ \sqrt{\sigma}_{1} {u}_{1} $ and the rows filter ...
4
Apart from the formulae, let us go back to their actual meaning, and how they are derived. Talking about convolution: this operation is inherent to Linear-Time-Invariant (LTI) systems. In other words: if
you want to analyse a system that is linear, and time-invariant,
or you want to apply a processing or a filter that does not vary in time or space
then ...
3
It is indeed possible to formulate this setting in terms of matrix-vector products. First, let us re-formulate your $x$ (notice throughout that I use bold letters for vectors and matrices):
$$x = \begin{bmatrix}\mathbf{x}_1 & \mathbf{x}_2 & \ldots & \mathbf{x}_8\end{bmatrix}$$
where $\mathbf x_k$ is the $k$ column of $x$.
I define the vertically ...
2
I am not sure there are "best" image processing or computer vision books to buy. The topics covered can be very wide, and some can be better on some aspect (morphology, segmentation, denoising, etc.).
Some sites recommend a hanful of such books, and link to their draft versions, as in 8 Books for Getting Started With Computer Vision. Indeed, a lot of ...
2
By default MATLAB simply draws a line from each point to each point, unless there are more points than pixels in which case each point or group of points within each pixel would represent each pixel shown.
Compare the following to see this:
This plots a line from x,y=1,2 to x,y= 5,7
plot([1 5], [2 7])
The above is the same as the following where a line ...
1
Those kind of algorithms are called Non Local algorithms.
The most known algorithms of this family is the - Non Local Means which is a decent Noise Reduction (Denoising) algorithm.
Until the Deep Learning boom, this approach has been extended and usually means working in the Patch Space of image - Patch Based Models and Algorithms for Image Denoising: A ...
1
There are different color spaces. Each of them has different coefficients for calculating gamma-corrected luma from gamma-corrected RGB values. You have listed coefficients for calculating luma according to ITU-R BT.709, ITU-R BT.601 and NTSC color spaces. There are many others as well, like BT.2020 used in consumer TVs for Wide Color Gamut.
1
clearly, these are very similar images
Both I and your arbitrarily picked measure for similarity would like to heartily contradict you, there.
It was you who picked SSIM, Structural SIMilarity, as measure; if that measure doesn't describe your own idea of similarity well enough, well, you might want to define what similarity is and come up with a ...
1
If the camera has a shallow depth of focus and the background is mostly blurry and the foreground is only moving at one focal plane, why not use a simpler method, such as Template Matching?
Since the printing head is changing its angle of view with respect to the lens as it moves in the $x,y$ dimensions, you might have to use more than one templates but ...
1
One of the most important classes of systems are Linear Time Invariant (or LTI) systems. These can fully described by either their transfer function or their impulse response (which are Fourier transforms of each other).
If you apply an input signal to an LTI system and you want calculate the output signal, you can simply convolve the input with the ...
1
For the 1-d case, I think that conv() is implemented in the direct domain while xcorr is implemented in the frequency domain.
This indicates that conv will be faster for small kernels, while xcorr will be faster when inputs are equal size.
I dont know if this still is the case, and if it extends to the 2-d case.
Operations that allows for native single-...
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