# A Convex Model for Edge-Histogram Specification with Applications to Edge-preserving Smoothing

arXiv: https://arxiv.org/abs/1806.08101 · HTML: https://mlsanity.com/paper/1806.08101/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2018.

## Built on by (most cited first, 2 of 2)

- [Image Watermarking of Generative Diffusion Models](https://mlsanity.com/paper/2502.10465/) (2025)
- [Dynamic watermarks in images generated by diffusion models](https://mlsanity.com/paper/2502.08927/) (2025)

## Abstract (arXiv)

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 [M. Mignotte. An energy-based model for the image edge-histogram specification problem. IEEE Transactions on Image Processing, 21(1):379--386, 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.