SIAM Journal on Numerical Analysis · 1994 · 218 citations · 25 references
ComputingComputer ScienceComputer VisionDigital ImagingMultiscale ModelingDigital Image ProcessingImage AnalysisImage ProcessingImage SegmentationTexture AnalysisVariational FormulationEnergyMergingMulti-scale SegmentationMultiscale SegmentationSegmentationTexture Segmentation
Segmentation algorithms typically involve multiple procedures such as split‑merge, region elimination, and boundary smoothing, each requiring several parameters. By introducing a minimizable energy, the authors reduce parameter dependence and develop a fast multiscale, multichannel variational merging algorithm with a pyramidal structure, applied to grey‑level and texture segmentation. The simple region‑merging algorithm achieves a local energy minimum, performs most segmentation tasks, runs in O(n log n) time, and yields effective grey‑level and texture segmentation as demonstrated by experiments.
Most segmentation algorithms are composed of several procedures: split and merge, small region elimination, boundary smoothing,..., each depending on several parameters. The introduction of an energy to minimize leads to a drastic reduction of these parameters. The authors prove that the most simple segmentation tool, the “region merging” algorithm, made according to the simplest energy, is enough to compute a local energy minimum belonging to a compact class and to achieve the job of most of the tools mentioned above. The authors explain why “merging” in a variational framework leads to a fast multiscale, multichannel algorithm, with a pyramidal structure. The obtained algorithm is $O(n\ln n)$, where n is the number of pixels of the picture. This fast algorithm is applied to make grey level and texture segmentation and experimental results are shown.
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