Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Shape Priors for Level Set Representations
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
A Higher-Order Active Contour Model for Tree Detection
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 02
A new phase field model of a 'gas of circles' for tree crown extraction from aerial images
CAIP'07 Proceedings of the 12th international conference on Computer analysis of images and patterns
ACIVS'07 Proceedings of the 9th international conference on Advanced concepts for intelligent vision systems
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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.