# Tag Archives: linear algebra

## Light transport matrices, SVD, spectral analysis, and matrix completion

In this post I’ll describe a small hike into the landscape of using linear algebra methods for analyzing seemingly non-algebraic problems, like light transport. This is very common in some domains of computer science / electrical engineering (seeing everything as … Continue reading

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## Procedural Kernel (Neural) Networks

Last year I worked for a bit on a fun research project that ended up published as an arXiv “pre-print” / technical report and here comes a few paragraph “normal language” description of this work. Neural Networks are taking over … Continue reading

## Comparing images in frequency domain. “Spectral loss” – does it make sense?

Recently, numerous academic papers in the machine learning / computer vision / image processing domains (re)introduce and discuss a “frequency loss function” or “spectral loss” – and while for many it makes sense and nicely improves achieved results, some of … Continue reading

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## Neural material (de)compression – data-driven nonlinear dimensionality reduction

In this post I come back to something I didn’t expect coming back to – dimensionality reduction and compression for whole material texture sets (as opposed to single textures) – a significantly underexplored topic. In one of my past posts … Continue reading

## Compressing PBR material texture sets with sparsity and k-SVD dictionary learning

Introduction In this blog post, I am going to continue exploration of compressing whole PBR texture sets together (as opposed to compressing each texture from the set separately) and using the fact that those textures are strongly correlated. In my … Continue reading

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## Dimensionality reduction for image and texture set compression

In this blog post I am going to describe some of my past investigations on reducing the number of channels in textures / texture sets automatically and generally – without assuming anything about texture contents other than correspondence to some … Continue reading

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## Separate your filters! Separability, SVD and low-rank approximation of 2D image processing filters

In this blog post, I explore separable convolutional image filters: how can we check if a 2D filter is separable, and how to compute separable approximations to any arbitrary 2D filter represented in a numerical / matrix form using SVD. Continue reading

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