I have recently being interested in the estimation of discontinuities or jumps from noisy signals or densities and spend some time reading "Image Processing and Jump Regression Analysis" by Peihua Qiu. I wonder if there is a similar book that presents more recent results ? Also the book focus on 2D image, is there any other book tackling higher dimensional settings ?
The subject is strongly connected with edge or boundary detection, which seems to be a central (and still active) subject in computer vision. But, all books or survey papers I have come across were mostly practical, presenting heuristics and numerical results. Is there any good references providing an overview of methods in edge detection with theoretical results (e.g. rigorous statistical study of the convergence property of the proposed estimator, such as "minimax study" of the convergence rates) ?