Deformable Pedal Curves and Surfaces: Hybrid Geometric Active Models for Shape Recovery
International Journal of Computer Vision
An Elliptic Operator for Constructing Conformal Metrics in Geometric Deformable Models
IPMI '01 Proceedings of the 17th International Conference on Information Processing in Medical Imaging
New Possibilities with Sobolev Active Contours
International Journal of Computer Vision
New possibilities with Sobolev active contours
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
On similarity-invariant fairness measures
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
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External energies of active contours are often formulated as Euclidean arc length integrals. In this paper, we show that such formulations are biased. By this we mean that the minimum of the external energy does not occur at an image edge. In addition, we also show that for certain forms of external energy the active contour is unstable when initialized at the true edge, the contour drifts away and becomes jagged. Both of these phenomena are due to the use of Euclidean arc length integrals. We propose a non-Euclidean arc length which eliminates these problems. This requires a reformulation of active contours where a single external energy function is replaced by a sequence of energy functions and the contour evolves as an integral curve of the gradient of these energies. The resulting active contour not only has unbiased external energy, but is also more controllable. Experimental evidence is provided in support of the theoretical claims. MRI is used as an example