Cost-based closed-contour representations Angel D. Sappa Computer Vision Center Edifici o Campus UAB 08193 Bellaterra, Barcelona, Spain E-mail: angel.sappa@cvc.uab.es Boris X. Vintimilla Vision and Robotics Center Department of Electrical and Computer Science Engineering Escuela Superior Politécnica del Litoral Campus Gustavo Galindo Km 30.5 vía Perimetral 09015863 Guayaquil, Ecuador Abstract. This paper presents an efficient technique for linking edge points in order to generate a closed-contour representation. It is based on the consecutive use of global and local schemes. In both cases it is assumed that the original intensity image, as well as its corresponding edge map, are given as inputs to the algorithm. The global scheme computes an initial representation by connecting edge points minimizing a global measure based on spatial informa- tion (3D space). It relies on the use of graph theory and exploits the edge points’ distribution through the given edge map, as well as their corresponding intensity values. At the same time spurious edge points are removed by a morphological filter. The local scheme fi- nally generates closed contours, linking open boundaries, by using a local cost function that takes into account both spatial and topo- logical information. Experimental results with different images, to- gether with comparisons with a previous technique, are presented. © 2007 SPIE and IS&T. DOI: 10.1117/1.2731799 1 Introduction Edge detection is the first and most important stage of hu- man visual process. 1 During the last few decades, several edge-point detection algorithms were proposed. In general, these algorithms are based on partial derivatives first and second derivative operators of a given image. Hence, the resulting edge maps are composed by a set of edge points arranged over the boundaries of the different regions con- tained in the image. Additionally, edge maps usually con- tain gaps as well as false edge points generated by noisy data. Although useful, edge points alone generally do not provide meaningful information about the image content, so a high-level structure is required e.g., to be used by scene understanding algorithms. From a given edge map the most direct high-level representation consists of com- puting closed contours—linking edge points by proximity, similarity, continuation, closure, and symmetry. Something that is very simple and almost a trivial action for the human being becomes a difficult task when it should be automati- cally performed. Broadly speaking, two different approaches for linking edge points have been proposed in the literature: 1 perceptual-based approaches e.g., Refs. 2–4 and 2 general-purpose approaches e.g., Refs. 5–7. The former ones are based on finding salient closed boundaries by us- ing Gestalt’s law of perception. These approaches are de- signed to solve a specific grouping problem, such as group- ing edge points into smooth closed contours, under quite constrained scenarios. They produce acceptable results on images for which their assumptions hold. On the contrary, the latter ones are able to handle any kind of images. No prior knowledge about the number of objects contained in the scene is required, nor is a constraint about maximum length of the gaps 2 nor about smoothness continuity 8 im- posed. It should be noticed that the main target of general- purpose approaches is to compute closed-contour represen- tations by linking edge points, which could be useful for a further high-level processing. Since only edge-point posi- tions are used, computed boundaries do not necessarily cor- respond to a boundary between two regions. The current paper falls into this second category. Notice that although perceptual-based approaches and general-purpose approaches pursue the generation of a closed-contour representation, their underlying philosophy is significantly different, since they tackle different goals and applications. In general, perceptual-based approaches incorporate mid-/high-level cues to link edges, while general-purpose approaches could be understood as low- level edge-linking methods that would need a further pro- cessing to generate high-level descriptions. Several general-purpose techniques have been presented for linking edge points in order to recover closed contours. According to the way edge map information is used, they can be divided into two categories: 1 local approaches, which work over every single edge point, and 2 global approaches, which work over the whole edge map at the same time. Alternatively, hybrid approaches that combine both techniques, or use not only edge map information but also enclosed information e.g., color, can be found. 6,9,10 In general, most of the techniques based on local information Paper 06120RR received Jul. 5, 2006; revised manuscript received Jan. 22, 2007; accepted for publication Jan. 29, 2007; published online Apr. 24, 2007. 1017-9909/2007/162/023009/9/$25.00 © 2007 SPIE and IS&T. Journal of Electronic Imaging 16(2), 023009 (Apr–Jun 2007) Journal of Electronic Imaging Apr–Jun 2007/Vol. 16(2) 023009-1