An Improved ‘Gas of Circles’ Higher-Order Active Contour Model and Its Application to Tree Crown Extraction

Abstract

A central task in image processing is to find the region in the image corresponding to an entity. In a number of problems, the region takes the form of a collection of circles, e.g. tree crowns in remote sensing imagery; cells in biological and medical imagery. In [1], a model of such regions, the ‘gas of circles’ model, was developed based on higher-order active contours, a recently developed framework for the inclusion of prior knowledge in active contour energies. However, the model suffers from a defect. In [1], the model parameters were adjusted so that the circles were local energy minima. Gradient descent can become stuck in these minima, producing phantom circles even with no supporting data. We solve this problem by calculating, via a Taylor expansion of the energy, parameter values that make circles into energy inflection points rather than minima. As a bonus, the constraint halves the number of model parameters, and severely constrains one of the two that remain, a major advantage for an energy-based model. We use the model for tree crown extraction from aerial images. Experiments show that despite the lack of parametric freedom, the new model performs better than the old, and much better than a classical active contour.

This work was partially supported by EU project IMAVIS (FP5 IHP-MCHT99), EU project MUSCLE (FP6-507752), Egide PAI Balaton, OTKA T-046805, and a HAS Janos Bolyai Research Fellowship. We thank the French National Forest Inventory (IFN) for the data.