Estimation of the noise level function for color images using mathematical morphology and non-parametric statistics

Noise level information is crucial for many image processing tasks, such as image denoising. To estimate it, it is necessary to find homegeneous areas within the image which contain only noise. Rank-based methods have proven to be efficient to achieve such a task. In the past, we proposed a method to estimate the noise level function (NLF) of grayscale images using the tree of shapes (ToS). This method, relying on the connected components extracted from the ToS computed on the noisy image, had the advantage of being adapted to the image content, which is not the case when using square blocks, but is still restricted to grayscale images. In this paper, we extend our ToS-based method to color images. Unlike grayscale images, the pixel values in multivariate images do not have a natural order relationship, which is a well-known issue when working with mathematical morphology and rank statistics. We propose to use the multivariate ToS to retrieve homogeneous regions. We derive an order relationship for the multivariate pixel values thanks to a complete lattice learning strategy and use it to compute the rank statistics. The obtained multivariate NLF is composed of one NLF per channel. The performance of the proposed method is compared with the one obtained using square blocks, and validates the soundness of the multivariate ToS structure for this task.