Region Growing and Related Methods

More than $30$ years have already passed since Zucker reviewed region growing algorithms [198]. Region growing is based on the propagation of an initial seed point according to a specific homogeneity criterion, iteratively increasing the size of the

Table 2.1: Single image based mammographic segmentation techniques indicating underlying (region, contour, clustering or model based) approach and used feature information (texture, gradient, grey-level or shape).

		Author	Year	Texture	Gradient	Grey-Level	Shape
		Huo [76]	$1995$			$\surd$	$\surd$
				Rangayyan [151]	$1997$
				Guliato [61]	$1998$
				Kupinski [95]	$1998$		$\surd$
				Qi [140]	$1998$
				Petrick [134]	$1999$		$\surd$
				Kwok [96]	$2002$	$\surd$
				Zheng []	$2003$
				Wei [188,189]	$2005$		$\surd$
			Kobatake [91]	$1996$			$\surd$
				Petrick [136,135]	$1996$		$\surd$
				Kobatake [90,89]	$1999$		$\surd$
				Sahiner [158,156]	$2001$		$\surd$
				Timp [177]	$2004$		$\surd$
			Brzakovic [20]	$1990$			$\surd$
				Kobatake [92,88]	$1994$
				Li [104]	$1995$	$\surd$
				Sahiner [157,155]	$1996$		$\surd$
				Undrill [181]	$1996$	$\surd$	$\surd$
				Chen [29]	$1997$	$\surd$
				Matsubara [117,116]	$1998$
				Goto [60]	$1998$		$\surd$
				Qian [141,142,143]	$1999$	$\surd$
				Heath [68]	$2000$	$\surd$
				Velthuizen [185]	$2000$
				Mudigonda [122]	$2001$		$\surd$
				Saha [154]	$2001$
				Zheng [195]	$2001$	$\surd$
				Li [105]	$2002$	$\surd$
				Hassanien [65]	$2004$
			Catarious [25]	$2004$			$\surd$
			Bellotti [8]	$2006$			$\surd$
		Lai [98]	$1989$			$\surd$	$\surd$
				Stathaki [167]	$1994$	$\surd$
				Karssemeijer [84]	$1996$		$\surd$
				Polakowski [139]	$1997$		$\surd$
				Jiang [81]	$1998$		$\surd$
				teBrake [174,175]	$1999$		$\surd$
				Constantidis [35,36]	$1999$
				Zwiggelaar [203]	$1999$		$\surd$
				Hatanaka [66]	$2001$		$\surd$
				Li [103]	$2001$	$\surd$
				Baydush [6]	$2003$
				Tourassi [179]	$2003$
				Campanini [24]	$2004$
				Cheng [31]	$2004$	$\surd$

region. Since those early days, region growing has received a number of improvements, mainly due to the integration of boundary information in the algorithm. As Freixenet et al. [54,124] reviewed, this information can be introduced before the growth step, using for example a controlled seed placement [9] or during it, like in active region algorithms [53,197].

Region growing algorithms have been widely used in mammographic mass segmentation. Since the early nineties, people from the University of Chicago studied the introduction of shape information into the homogeneity criterion. With the aim to integrate the radiologists experiences, Huo et al. [76] developed a semi-automatic region growing approach, in which the growing step was automatically computed after a radiologist had manually placed the seed point. Later, Kupinski and Giger [95] compared this initial approach with two improved versions. The first one incorporated the Radial Gradient Index, which is a measure of the average proportion of gradient which are radially directed outwards (for a circular region the radial gradient index is equal to one). The second one was based on a probabilistic method in which the probability of belonging to one region was modeled by a non-Gaussian distribution (using a kernel distribution), whilst the background was modeled using a uniform probability. They showed that this last parametric version performed better compared to both other approaches. A different approach was proposed by Guliato et al. [61], who implemented a fuzzy version of the region growing algorithm. In contrast with the methods from Chicago, this approach was pixel based (the homogeneity criterion is evaluated for each pixel), and no prior shape information was considered. Guliato et al.'s method was based on considering the uncertainty present around the boundaries of a tumour region, with the aim to preserve the transition between mass and normal tissue. An alternative approach was proposed by Petrick et al. [134], who introduced gradient information into the region growing algorithm with the objective to reduce merging between adjacent and overlapping structures. Initially, the algorithm selects seeds using local maxima in the grey-scale image. In a subsequent step, a gradient image is constructed by using a frequency-weighted Gaussian filtering. With this image, the thresholds of the regions bounded by the edges are extracted. In common with the Chicago approach, Petrick et al. aggregate groups of pixels with similar characteristics (using thresholds), but, in contrast, they do not use shape information in the homogeneity criterion.

Other researchers spent their efforts improving the region growing algorithm by identifying the optimal set of initial seeds. Qi and Snyder [140] used Bézier splines to interpolate histograms, from which they extracted threshold values at local maxima. Zheng et al. [] used as starting point an edge image. This image was obtained by subtracting two blurred images obtained by using Gaussian filtering of the original image using a large difference in kernel size.