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As shown in your examples, you have used an odded-sized kernel. Those are very common in image processing. Plus, they can ease the visualization of what happens. If the kernel is $(2\kappa+1)\times (2\kappa+1)$, you can think of superimosing the center of the flipped kernel over each pixel, as known on the Matlab 2D convolution:
So the equation becomes:
$...
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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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If it is a color camera, then typically there is a Bayer filter mosaic in front of the sensor:
Figure 1. Bayer filter (with cutout) in front of a sensor. Image credit: Colin M.L. Burnett.
Perhaps the grayscale mode pixels are simply the sensor element outputs, giving the repeating pattern for a solid color area. You can first debayer the image into a color ...
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It looks like that is a color camera with the Bayer pattern, and the color camera data is directly used as grayscale data, as if it was coming from a grayscale camera. If it is a color camera, the color camera data should be de-Bayerized first (and smoothed etc processing) to get color RGB data pixels as usual, and then the RGB data can be converted to ...
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You can obtain pretty good results by just thresholding the image at a high intensity (since your text appears always to be white) and do a closing operation to close the gaps:
# convert to grayscale
img = cv2.imread('OCR.jpg')
gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
# threshhold
ret,bin = cv2.threshold(gray,245,255,cv2.THRESH_BINARY)
# closing
...
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The easiest approach would be writing each case using Matrix Form of the convolution.
In this answer we assume the discrete convolution is applied only on valid support (Matching MATLAB's valid parameter for the convolution).
Namely, given $ x \in \mathbb{R}^{m \times n} $ and $ h \in \mathbb{R}^{k \times l} $ then $ h \ast x \in \mathbb{R}^{ \left( m - k + ...
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No transform is required for that kind of thing except making sure that the rays of light hit the lens head on.
This is only possible when the subject is far away enough from the camera and for a narrow range of its field of view.
In other words, the end result image we are talking about here is composed of vertical projections of 3D points right on the ...
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The problem in your implementation is that it returns the tensor of float, while an image must be a tensor of int. Because of that, your rendering library, which I assume is matplotlib, cannot correctly plot an image.
To fix that you need to specify the type of final_img explicitly. That is, you need to add a parameter dtype=np.int when creating final_img, ...
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Vanilla implementation of each method for image of size m x n and kernel of size k x l will yield:
Spatial Domain Convolution - O(mnkl) as for each pixel in the image we do kl multiplications (Additions are discarded).
Frequency Domain Convolution - O(mn log(mn) + mn) as the complexity of the FFT is mn log(mn) and we add the multiplication (You could add ...
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In image denoising far more important then the noise distribution is the noise spatial correlation properties and the prior about the image.
Let's try building some cases and dealing with them.
The model is:
$ y = x + n $
Where $ x $ is the clan image, $ n $ is the Poisson Noise (With mean $ \lambda $) and $ y $ is the noisy image.
Noise Is Poisson ...
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