Robustnost vůči transformacím v počítačovém vidění: invariantní &amp; equivariantní neuronové sítě

Karella, Tomáš

This Thesis addresses the fundamental challenge of transformation robustness in com- puter vision, focusing on designing neural networks that are inherently invariant to rota- tions and translations. While data augmentation is commonly used to achieve robustness, it lacks mathematical guarantees and requires large amounts of data samples. We build on an alternative approach that embeds transformation robustness directly into the design of neural networks using established group theory principles. This method offers signif- icant advantages, including theoretical guarantees of invariance, reduced computational complexity, improved sampling efficiency, and better generalization to previously unseen transformations. Our major contributions include: (1) two novel neural network archi- tectures that provide end-to-end invariance to rotations and translations, (2) integration of classical hand-crafted features into modern neural networks to enhance transformation robustness, and (3) empirical validation demonstrating improved reliability and efficiency in various computer vision tasks.

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