Real-Time Time-to-Collision from Variation of Intrinsic Scale

Nègre, Amaury; Braillon, Christophe; Crowley, James L.; Laugier, Christian · 2008 · Crossref

DOI: 10.1007/978-3-540-77457-0_8

archive: archived pipeline: cataloged verified

Get this paper ↗ (DOI — opens at the source; we link to it, we don't host it)

Summary

This paper addresses the challenge of estimating Time-to-Collision (TTC) for autonomous vehicles in dynamic environments, a critical variable for obstacle avoidance. While TTC can theoretically be derived from optical flow, existing methods relying on dense optical flow estimation or focus of expansion are often impractical for real-time applications, particularly when multiple objects move independently. The authors propose a novel, computationally efficient approach that estimates TTC by measuring the rate of change of the "intrinsic scale" of image features, utilizing an uncalibrated camera. The method relies on the geometric principle that the inverse of an object's image size is proportional to its distance from the camera. Consequently, TTC can be calculated from the derivative of this image size. To robustly estimate local feature size, the authors employ a Laplacian scale space representation, where intrinsic scale is determined by the sigma value at which the Laplacian exhibits local extrema. To handle image registration and tracking, the approach detects "natural interest points" for compact features and extends this to "natural interest lines" (ridges) for elongated objects, which are common in urban environments. Ridge detection involves computing principal curvature directions via the Hessian matrix and identifying extrema in those directions. Tracking is achieved through a correlation process that matches features across frames based on spatial distance, scale, significance (Laplacian value), and second-order moments, refined by a Kalman Filter. Experimental validation was conducted using a moving vehicle equipped with both a camera and a laser range finder. The system tracked a reflective target mark, comparing the TTC derived from the visual intrinsic scale method against the ground truth provided by the laser scanner. The experiments demonstrated that the visual method yields reliable TTC estimates with low computational cost, requiring approximately 50 milliseconds per frame on a 3GHz Pentium 4 processor. Results showed that after a brief initialization period, the estimated TTC closely matched the laser-derived values, confirming the linearity of the inverse scale with distance during constant-speed approach. The significance of this work lies in providing a simple, robust, and real-time solution for TTC estimation that leverages the wide field of view and low cost of cameras without requiring complex optical flow calculations. The use of a pyramidal algorithm ensures efficiency, making it suitable for autonomous navigation. The authors conclude that while the current model assumes constant speed, future work should aim to generalize the computation to more image points to create a continuous TTC field and incorporate more complex motion models.

Provenance

The full processing record for this entry. Every stage of this paper's journey through the pipeline is logged — what ran, with which tool and model, how many attempts it took, and when it last completed.

Summary generated by qwen3.6-27b-prismaquant on 2026-06-26; verification: verified.

Topics

Ranked by relevance to this paper. Hover a topic for its definition.

• time to collision looming