A variational approach for exact histogram specification
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
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PerMIn'12 Proceedings of the First Indo-Japan conference on Perception and Machine Intelligence
MCV'12 Proceedings of the Second international conference on Medical Computer Vision: recognition techniques and applications in medical imaging
Exact Histogram Specification for Digital Images Using a Variational Approach
Journal of Mathematical Imaging and Vision
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Pattern Recognition
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Journal of Mathematical Imaging and Vision
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While in the continuous case, statistical models of histogram equalization/specification would yield exact results, their discrete counterparts fail. This is due to the fact that the cumulative distribution functions one deals with are not exactly invertible. Otherwise stated, exact histogram specification for discrete images is an ill-posed problem. Invertible cumulative distribution functions are obtained by translating the problem in a K-dimensional space and further inducing a strict ordering among image pixels. The proposed ordering refines the natural one. Experimental results and statistical models of the induced ordering are presented and several applications are discussed: image enhancement, normalization, watermarking, etc.