Implement Gaussian Filtering Using Sparse Matrix Instead of Built-in Functions

[zhaozhijun714]

Background

Currently, I need to perform Gaussian filtering on images, but I want to avoid using MATLAB's built-in functions. Given an image of size N x N, my idea is to construct a sparse matrix where both dimensions are N*N. Each column of this matrix should contain the values of the Gaussian kernel related to the current pixel.

Task

• Implement the construction of such a sparse matrix for Gaussian filtering.
• The matrix should be of size NN x NN, where N is the image width/height.
• Each column should represent the Gaussian kernel for the corresponding pixel.
• The solution should not use MATLAB's built-in Gaussian filtering functions.

Expected Outcome

• MATLAB or Python code to create and apply the sparse matrix for filtering.
• Comments explaining the construction and application process.
• An example usage demonstrating the filter on a sample image.

Additional Notes

• This issue is for algorithm implementation and should avoid built-in high-level Gaussian filter functions.
• The approach should be efficient and leverage sparse matrix operations for large images.

[villekf]

I can see why this would be useful, but I have some questions.

First, is this a feature request or something you are working on?

Second, any particular reason why you want to avoid built-in functions? I can understand that this method allows for unique filter size/shape for each voxel. However, it can also become computationally heavy if the dimensions are large.

[zhaozhijun714]

Dear developer,

Thank you for your response.

This is both a feature request and something I’m currently working on. At present, the PSF modeling uses a spatially invariant Gaussian kernel. My goal is to extend this to a spatially varying Gaussian kernel so that different regions within the FOV can be modeled with different gaussian function.

Best regards

[villekf]

Thanks for the clarification. I won't be able to dedicate time for this feature, but if you need technical help with something, I should be able to assist to some extent.

Good luck and let me know if you have any questions.