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

TL;DR

Log Conformal Maps (LCM) is proposed, a method leveraging the logarithmic function to approximate perspective distortions with fewer parameters and reduced computational complexity, and demonstrates seamless integration with person re-identification and improved the performance.

Abstract

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 Möbius transform for mitigating perspective distortions (MPD) to synthesize perspective distortions without estimating camera parameters. Möbius 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.

Figures (10)

• Figure 1: Log conformal Mapping Method (LCM). LCM obtains four perspective distorted views using auxiliary operations with Log Conformal transform.
• Figure 2: Comparison of LCM with MPD method chhipa2024m across probability values. Red line shows standard ResNet50. LCM outperform ResNet50 model trained on ImageNet and matches the performance with MPD. MPD results from chhipa2024m.
• Figure 3: Comparison of self-supervised trained LCM+SimCLR with MPD+SimCLR method chhipa2024m across probability values. Red line shows standard ResNet50. LCM outperform ResNet50 model trained on ImageNet and matches the performance with MPD. MPD results are reported from chhipa2024m.
• Figure 4: Comparison of linear evaluation performance on self-supervised trained models. (Left): original SimCLR chen2020simple, LCM+SimCLR and MPD+SimCLRchhipa2024m on original ImageNet and ImageNet-PD subsets. Performance on ImageNet-PD is average over all four subsets. (Right): Comparing original DINO caron2021emerging, LCM+DINO and MPD+DINO chhipa2024m on original ImageNet and ImageNet-PD subsets. Performance on ImageNet-PD is average over all subsets.
• Figure 5: Activation maps: (Left) beaker example (n02815834) in ImageNet-PD subsets comparing MPD and LCM in self-supervised learning method SimCLR chen2020simple. (Right) Staffordshire bullterrier example (n02093256) in ImageNet-PD subsets comparing MPD and LCM in self-supervised learning method DINO caron2021emerging. Reported result for MPD is used and same example were used for comparison.

Theorems & Definitions (2)

• theorem thmcountertheorem
• proof