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LCM: Log Conformal Maps for Robust Representation Learning to Mitigate Perspective Distortion

Perspective distortion (PD) leads to substantial alterations in the shape, size, orientation, angles, and spatial relationships of visual elements in images. Accurately determining camera intrinsic and extrinsic parameters is challenging, making it hard to synthesize perspective distortion effectively. The current distortion correction methods involve removing distortion and learning vision tasks, thus making it a multi-step process, often compromising performance. Recent work leverages the M\"obius transform for mitigating perspective distortions (MPD) to synthesize perspective distortions without estimating camera parameters. M\"obius transform requires tuning multiple interdependent and interrelated parameters and involving complex arithmetic operations, leading to substantial computational complexity. To address these challenges, we propose Log Conformal Maps (LCM), a method leveraging the logarithmic function to approximate perspective distortions with fewer parameters and reduced computational complexity. We provide a detailed foundation complemented with experiments to demonstrate that LCM with fewer parameters approximates the MPD. We show that LCM integrates well with supervised and self-supervised representation learning, outperform standard models, and matches the state-of-the-art performance in mitigating perspective distortion over multiple benchmarks, namely Imagenet-PD, Imagenet-E, and Imagenet-X. Further LCM demonstrate seamless integration with person re-identification and improved the performance. Source code is made publicly available at https://github.com/meenakshi23/Log-Conformal-Maps.

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