Abstract
The goal of edge-histogram specification is to find an image whose edge image has a histogram that matches a given edge-histogram as much as possible. Mignotte has proposed a non-convex model for the problem in 2012. In his work, edge magnitudes of an input image are first modified by histogram specification to match the given edge-histogram. Then, a non-convex model is minimized to find an output image whose edge-histogram matches the modified edge-histogram. The non-convexity of the model hinders the computations and the inclusion of useful constraints such as the dynamic range constraint. In this paper, instead of considering edge magnitudes, we directly consider the image gradients and propose a convex model based on them. Furthermore, we include additional constraints in our model based on different applications. The convexity of our model allows us to compute the output image efficiently using either Alternating Direction Method of Multipliers or Fast Iterative Shrinkage-Thresholding Algorithm. We consider several applications in edge-preserving smoothing including image abstraction, edge extraction, details exaggeration, and documents scan-through removal. Numerical results are given to illustrate that our method successfully produces decent results efficiently.
Highlights
Histogram specification is a process where the image histogram is altered such that the histogram of the output image follows a prescribed distribution
We propose a convex model that can include additional constraints based on different applications in edge-preserving smoothing
We propose a convex model for applications in edge-preserving smoothing
Summary
Histogram specification is a process where the image histogram is altered such that the histogram of the output image follows a prescribed distribution. To match the edge-histogram, the author in [11] proposed the following non-convex model for the problem. We propose a convex model that can include additional constraints based on different applications in edge-preserving smoothing. We propose a convex model for applications in edge-preserving smoothing. The simplicity of our model allows us to incorporate different useful constraints such as the dynamic range constraint; the convexity of our model allows us to compute the output efficiently by Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) [45] or Alternating Direction Method of Multipliers (ADMM) [46,47]. We introduce different edge-histograms and suitable constraints in our model, and apply them to different imaging tasks in edge-preserving smoothing, including image abstraction, edge extraction, details exaggeration, and scan-through removal.
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