Extremal Contours: Gradient-driven contours for compact visual attribution

TL;DR

This paper introduces a training-free, gradient-driven contour method for visual model explanations that produces compact, interpretable, and stable regions, outperforming dense perturbation masks in relevance and complexity.

Contribution

It presents a novel, optimization-free contour explanation technique using Fourier parameterization, improving interpretability and robustness over existing dense mask methods.

Findings

Matches extremal fidelity of dense masks on ImageNet

Produces more compact, interpretable regions

Improves relevance mass by over 15% on DINO models

Abstract

Faithful yet compact explanations for vision models remain a challenge, as commonly used dense perturbation masks are often fragmented and overfitted, needing careful post-processing. Here, we present a training-free explanation method that replaces dense masks with smooth tunable contours. A star-convex region is parameterized by a truncated Fourier series and optimized under an extremal preserve/delete objective using the classifier gradients. The approach guarantees a single, simply connected mask, cuts the number of free parameters by orders of magnitude, and yields stable boundary updates without cleanup. Restricting solutions to low-dimensional, smooth contours makes the method robust to adversarial masking artifacts. On ImageNet classifiers, it matches the extremal fidelity of dense masks while producing compact, interpretable regions with improved run-to-run consistency. Explicit area control also enables importance contour maps, yielding a transparent fidelity-area profiles. Finally, we extend the approach to multi-contour and show how it can localize multiple objects within the same framework. Across benchmarks, the method achieves higher relevance mass and lower complexity than gradient and perturbation based baselines, with especially strong gains on self-supervised DINO models where it improves relevance mass by over 15% and maintains positive faithfulness correlations.