Image Segmentation Based on a Two-Dimensional Histogram

Abstract

Image segmentation refers to the partitioning of an image into non-overlapping different regions with similar attributes. For gray level images, the most basic attribute used is the luminance amplitude, and for color or multispectral images, color or information components are used. Various methods are found in the literature and are roughly classified into several categories according to the dominant features they employ. This includes edge-based methods (Zugaj & Lattuati, 1998), region growing methods (Tremeau & Borel, 1998; Schettini, 1993), neural networks methods, physics-based methods (Maxwell & Shafer, 1996; Bouda et al. 2008) and histogram thresholding methods (Sezgin & Sankur,2004). It is demonstrated that in unsupervised classification cases the histogram threshold method is a good candidate for achieving segmentation for a wide class of gray level images with low computation complexity (Cheng et. al., 2001). This method ignores the spatial relationship information of the pixels that can give improper results. Abutaleb’s work (Abutaleb, 1989) presents another type of 2D gray level histogram. It is formed by the Cartesian product of the original 1D gray level histogram and 1D local average gray level histogram generated by applying a local window to each pixel of the image and then calculating the average of the gray level within the window. Zhang and al. (Zhang & Zhang, 2006) proposed using a minimum gray value in the 4-neighbor and the maximum gray value in the 3×3 neighbor except pixels of the 4-neighbor. This method’s main advantage is that it does not require prior knowledge regarding the number of objects in the image, and classical and fast gray level image processing algorithms can be used to cluster the 2D histogram (Clement, 2002). For color or multispectral images, the one-dimensional (1D) histogram method detracts from the fact that a color cluster is not always present in each component and the combination of the different segmentations cannot catch this spatial property of colors (Clement & Vigouroux, 2001). It also does not take into account the correlation between components (Uchiyama & Arbib, 1994). Therefore multiple histogram-based thresholding is required. However, in a full multi-dimensional manner, the three-dimensional histogram (3D-histogram) method is handicapped by data sparseness, the complexity of the search algorithm (Lezoray & Cardot,2003) and a huge memory space (Clement & Vigouroux, 2001). An interesting alternative method lies with the use a partial histogram (2D-histogram)(