Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A new characterization of three-dimensional simple points
Pattern Recognition Letters
Simple points, topological numbers and geodesic neighborhoods in cubic grids
Pattern Recognition Letters
Region-based strategies for active contour models
International Journal of Computer Vision
Region Competition: Unifying Snakes, Region Growing, and Bayes/MDL for Multiband Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A level set algorithm for minimizing the Mumford-Shah functional in image processing
VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)
A Statistical Approach to Snakes for Bimodal and Trimodal Imagery
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Modified curvature motion for image smoothing and enhancement
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
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Here we present a segmentation algorithm that uses multi-scale diffusion with the Mumford-Shah model. The image data inside and outside a surface is smoothed by minimizing an energy functional using a partial differential equation that results in a trade-off between smoothing and data fidelity. We propose a scale-space approach that uses a good deal of diffusion as its coarse scale space and that gradually reduces the diffusion to get a fine scale space. So our algorithm continually moves to a particular diffusion level rather than just using a set diffusion coefficient with the Mumford-Shah model. Each time the smoothing is decreased, the data fidelity term increases and the surface is moved to a steady state. This method is useful in segmenting biomedical images acquired using high-resolution confocal fluorescence microscopy. Here we tested the method on images of individual dendrites of neurons in rat visual cortex. These dendrites are studded with dendritic spines, which have very small heads and faint necks. The coarse scale segments out the dendrite and the brighter spine heads, while avoiding noise. Backing off the diffusion to a medium scale fills in more of the structure, which gets some of the brighter spine necks. The finest scale fills in the small and detailed features of the spines that are missed in the initial segmentation. Because of the thin, faint structure of the spine necks, we incorporate into our level set framework a topology preservation method for the surface which aids in segmentation and keeps a simple topology.