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31 views

How does the “additive operator splitting” exactly work?

I am reading about the non-linear (or non-homogenous) diffusion method (aka anistropic diffusion method). There are several ways of implementing this method. In all cases, we first need to discretise ...
0
votes
1answer
31 views

What is the difference between domain and range filtering?

In the context of image processing, I have heard the expressions "domain filtering" and "range filtering". What do these terms refer to? What is the difference between them?
2
votes
3answers
345 views

How to Classify Image Filter as Low Pass Filter (LPF) or High Pass Filter (HPF)?

I am currently reading on the topics of image filtering and convolution kernels. While the process of convolution is clear to me, I do not understand, how one arrives at the statement, that a certain ...
1
vote
1answer
739 views

What are the advantages and disadvantages separability of Gaussian 2D filter?

I know separability of a Gaussian filter enhances the computational complexity from $\mathcal{O}(L^2*N*M) \to \mathcal{O}((L*N*M)$. How this really reflect on my program? I suppose the number of for ...
0
votes
2answers
712 views

Convolution in spatial domain is multiplication in frequency domain

I have to prove convolution in spatial domain = multiplication in frequency domain using two matrices. $$ x(m, n) = \begin{bmatrix} 1 && 2 \\ 3 && 4 \end{bmatrix} $$ $$ h(m, n) = \...
1
vote
1answer
361 views

Image zoom out using Gaussian blur and downsampling

I am trying to implement a simple zoom out algorithm using two steps: The image is blurred using gaussian convolution of standard deviation $0.8\sqrt{{\tt zoomfactor}^2-1}$ as we saw in class. The ...
1
vote
1answer
5k views

Differences between low-pass, band-pass, notch filters

I'm studying image processing and I know that there are different filters you can apply. I don't understand the difference between the low-pass/bandpass/notch filter (or high-pass/band-reject/notch). ...
1
vote
1answer
2k views

What is the significance of Butterworth filter in image processing?

Filters like mean,median,gaussian,bilateral and adaptive forms of these filters are used commonly in image processing but not Butterworth filter. The reasons I could think of are a) Butterworth ...
0
votes
0answers
255 views

Prediction-error filter for images

I am interested in studying local pixel value dependencies in images and I am wondering if it exists a general form of prediction-error convolutional filter that is able to suppress the image's ...
0
votes
2answers
222 views

Easy way to get rid of noise in a hand drawing

I would like to take a user's hand drawn input, and filter out "noise", aka small sketches or blobs, where the user might have screwed up and accidentally touched his hand to the drawing device, or ...
0
votes
1answer
611 views

Filter and crop an image

I am a big fan of fft convolution. So, I mostly try to avoid non-fft convolution. Suppose, I am trying to convolute an image with another image. Suppose the first image is $512\times 512$, and, the ...
1
vote
0answers
41 views

Proximal operator of image Laplacian

Let $\alpha, \beta > 0$ and $\Delta := \nabla^T \nabla$ be the discrete laplacian operator, $$\nabla: \mathbb{R}^{n_x \times n_y \times n_z} \rightarrow \mathbb{R}^{3 \times n_x \times n_y \times ...
1
vote
1answer
2k views

What is a 'notch' in image processing?

I cannot find out what does "notch" means in image processing? We have selective filters that one of the best of them is Notch filters. but what does the concept of "Notch"? why they are called "...
1
vote
3answers
43 views

Texture-like measures for quantifying density of data in binary images

Consider the following black-and-white image. It depicts a freehand sketch. I wish to characterize the "density" of sketch strokes. For e.g. the hair strokes are densely grouped together. So are ...
1
vote
1answer
90 views

Contour based blurring

Suppose I have an image of a cat and a binary mask image corresponding to cat's location as shown I would like to blur the image region surrounding the cat but as a function of distance from the cat'...
3
votes
4answers
7k views

difference between mean filter and order statistic filter

I am working on my paper about comparing between mean filter and ordering statistics filter, The mean filter is contraharmonic mean filter and the ordering statistic filter is alphatrimmed mean filter....
0
votes
2answers
5k views

How to Calculate Gaussian Kernel for a Small Support Size?

How to calculate the values of Gaussian kernel? I think I understand the principle of it weighting the center pixel as the means, and those around it according to the $\sigma$ but what would each ...
1
vote
1answer
783 views

How does kernel work in unsharp masking?

I applied the kernel below to the picture for unsharp masking k = [-1 -1 -1; -1 8 -1; -1 -1 -1] I got ! Then I changed 8 to 14. And I got How does kernel work ...
2
votes
1answer
170 views

Morphological Gradient Versus Linear Gradient in Image Processing

To obtain the gradient from an image, one can use a linear filter that for example is derrived from the derrivative of a gaussian. Then convolving the image with this linear filter gives you the ...
0
votes
1answer
327 views

use scale space representation to filter one image

Currently I hope to use scale space representation to filter one image. Features in one image can be filtered using an Gaussian smooth filter with one optimal sigma. It means different features in one ...
1
vote
1answer
104 views

Blurring transfer function of image

I need help solving the following blurring function question.Assume an image $f(x,y)$ is moving in front of a camera so that $𝑥_0(𝑡)$ and $𝑦_0(𝑡)$ are the time-varying components of motion in the ...
0
votes
1answer
309 views

Role of the rank of the filter mask matrix in image processing?

I'm reading a material where it says that a filter mask or kernel can be separable if the matrix of the filter mask has a rank 1. The two slides which describes this are as below: Reading these ...
2
votes
2answers
294 views

Anisotropic Diffusion Filter - Intuition Behind Parameters

I need to know what is iteration and divergence in anisotropic diffusion filter technique. Isotropic diffusion $$\frac{\partial I(x, y, z)}{\partial t}={\rm div}\left[c\cdot \nabla I\left(x, y, ...
14
votes
3answers
31k views

What is the difference between linear and non-linear filters?

How a mean filter is called as linear filter and a median filter is called as non linear filter? I understand how a mean and median filter operates, but I was not able to relate with the term linear ...
0
votes
2answers
388 views

Apply Singular Value Decomposition on Gabor filters

According to my question in this link, I applied (with a big help from lennon310) the separability of Gabor filters of any orientation. The only disadvantage of this method is the convolution in the ...
0
votes
1answer
587 views

Filtering an image with two gabor filters

I have an image of size 160x160 of pixels. I am trying to convolve this image with two Gabor filters of different scales (7 and 9 respectively) but with the same orientation. I red in an article the ...
3
votes
1answer
1k views

Is it not possible to perform non-linear filtering in frequency domain?

This link contains the following statement: In contrast to the frequency domain, it is possible to implement non-linear filters in the spatial domain. In this case, the summations in the ...
8
votes
3answers
15k views

How do convolutions become matrix multiplications?

I know this question may not be very relevant to programming, but if I don't understand the theory behind image processing I'll never be able to implement something in practice. If I got it right ...