Scale-dependent hierarchical unsupervised segmentation of textured images Antonio Bandera * , Cristina Urdiales, Fabian Arrebola, Francisco Sandoval Departamento de Tecnolog  ia Electr onica, E.T.S.I. Telecomunicaci on, Universidad de M alaga, Campus de Teatinos, 29071 M alaga, Spain Received 12 August 1999; received in revised form 12 September 2000 Abstract This paper presents a new three-staged texture-based segmentation method that, using multiresolution techniques, provides high computational speed. The main novelty of the approach is that spatial proximity has a progressively decreasing importance on lower resolution levels when hierarchically segmenting the data structure. The method achieves low error rates and it does not require any knowledge about the number of textures in the image. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: Texture; Hierarchical segmentation; Scale-dependent pyramid stabilisation; Unsupervised class fusion 1. Introduction Industrial applications of texture-based image segmentation in ®elds like medical image process- ing or real image object detection have been lim- ited because of the enormous computational load related to such a process, the alternative being the use of an expensive and complex dedicated pro- cessor. Texture-based segmentation algorithms split the image into several regions yielding dierent statistical behaviours. Such methods assume that the statistics of each region are stationary and that each region extends over a signi®cant area. How- ever, most regions do not present stationary fea- tures, and they can also be too small sized. Therefore, methods relying on an a priori knowl- edge of the number of textures in the image (Pie- tikainen and Rosenfeld, 1981; Schwartz and Quinn, 1996; Puzicha and Buhman, 1997) often fail, because if any unexpected texture region ap- pears, like the ones related to shadows or bound- aries, a wrong fusion of two non-related regions is forced. Unsupervised segmentation (Bouman and Liu, 1991; Hu and Dennis, 1994; Ojala and Pie- tikainen, 1997) does not rely on such a knowledge, but it is obviously slower, because it requires a computationally expensive additional stage to calculate the correct number of regions in the im- age (Hu and Dennis, 1994). A common choice to speed up segmentation processes is to use multiresolution structures. Most multiresolution methods work in a coarse-to-®ne way (Pietikainen and Rosenfeld, 1981; Bouman and Liu, 1991; Schroeter and Big un, 1995; Puzicha and Buhman, 1997). They typically present two problems: (i) they adopt the same cost functions at Pattern Recognition Letters 22 (2001) 171±181 www.elsevier.nl/locate/patrec * Corresponding author. Tel.: +34-5-213-2844; fax: +34-5- 213-1447. E-mail address: bandera@dte.uma.es (A. Bandera). 0167-8655/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 8 6 5 5 ( 0 0 ) 0 0 1 0 3 - 3