SHCF: A supervised hierarchical clustering approach to remove high density salt and pepper noise from black and white content digital images

When a digital image with a lot of healthy salt and pepper (SP) pixels is corrupted by salt and pepper noises (SPNs) current solutions for SPN removal have difficulty distinguishing the healthy SP pixels from the noisy ones. Consequently, they often exhibit low performance when the original image contains patches of salt or/and pepper pixels. This paper introduces a new SPN removal approach called Supervised Hierarchical Clustering Filter (SHCF) capable of removing high density SP noises. SHCF first assigns a label to each pixel: W to white, B to black and N to the remaining pixels. Next, a supervised hierarchical clustering (SHC) approach is employed to build a tree of pixels called SHC-tree. SHC-trees are constructed maximizing cluster purities in the intermediate nodes. After the tree has been fully built, it is trimmed by extracting 100% purity clusters from the tree. Clusters with black or white pixels of size smaller than a user-defined minimum cluster size threshold are considered outliers and their pixels are marked as corrupted. The rest of the pixels in the image are marked as healthy. In its final step—unlike existing approaches—SHCF uses a replacement method that is order independent; that is, the order in which the corrupt pixels are replaced does not have any bearing on the final restoration result. We conducted experiments on images containing a lot of salt/pepper pixels as well as on standard test images. The results show that SHCF exhibits competitive performances compared to its direct competitors on standard test images. At high density noise level, it outperforms its competitors on average by 16% on images containing large amount of black and white pixels.