Linked Edges as Stable Region Boundaries* Michael Donoser, Hayko Riemenschneider and Horst Bischof This work introduces an unsupervised method to detect stable edges in grayscale images. In contrast to common edge detection algorithms as Canny, which only analyze local discontinuities in image brightness, our method integrates mid-level information by analyzing regions that support the local gradient magnitudes. We use a component tree where every node contains a single connected region obtained from thresholding the gradient magnitude image. Edges in the tree are defined by an inclusion relationship between nested regions in different levels of the tree. Region boundaries which are similar in shape (i.e. have a low chamfer distance) across several levels of the tree are included in the final result. The proposed detection algorithm labels all identified edges during calculation, thus avoiding the cumbersome post-processing of connecting and labeling edge responses. Abstract References [1] L. Najman and M. Couprie, Quasi-Linear Algorithm for the Component Tree, SPIE Vision Geometry XII, 2004 [2] J. Matas, O. Chum, M.Urban and T. Pajdla, Robust Wide Baseline Stereo from Maximally Stable Extremal Regions, Proceedings of British Machine Vision Conference (BMVC), 2002 [3] J. Canny, A computational approach to edge detection, IEEE Transactions Pattern Analysis Machine Intelligence (PAMI), 8(6):679–698, [4]D. Martin, C. Fowlkes, and J. Malik, Learning to detect natural image boundaries using local brightness, color, and texture cues, IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), 26(5):530–549, References [1] L. Najman and M. Couprie, Quasi-Linear Algorithm for the Component Tree, SPIE Vision Geometry XII, 2004 [2] J. Matas, O. Chum, M.Urban and T. Pajdla, Robust Wide Baseline Stereo from Maximally Stable Extremal Regions, Proceedings of British Machine Vision Conference (BMVC), 2002 [3] J. Canny, A computational approach to edge detection, IEEE Transactions Pattern Analysis Machine Intelligence (PAMI), 8(6):679–698, [4]D. Martin, C. Fowlkes, and J. Malik, Learning to detect natural image boundaries using local brightness, color, and texture cues, IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), 26(5):530–549, Conclusion We proposed an unsupervised edge detection method, which in contrast to purely analyzing local discontinuities of image brightness, additionally considers adjacent regions which support the local gradient magnitudes. We showed that all required steps are quite efficient and that the method reduces clutter while preserving the most important edges. All edges are automatically linked and labeled during calculation. Institute for Computer Graphics and Vision, Graz University of Technology Component Tree on Gradient Magnitudes Overview Finding Stable Region Boundaries Component Tree [1] Unique, tree-shaped data structure Build for graph with node values coming from a totally ordered set We appy it to gradient magnitude image Thresholding magnitude image at all possible magnitude values Node: Connected region within threshold result Edge: Inclusion relationship between nested regions at different thresholds Considered edges are outer boundaries of node regions (shown in red) Experiments: ETHZ and Weizmann horses Comparison on ETHZ (5 classes) and Weizmann horses (1 class) Comparison to ground truth object segmentation results Analysis using Precision/Recall and F-Values 23rd IEEE Conference on Computer Vision and Pattern Recognition (CVPR) CVPR 2010 Results Unsupervised edge detection Analysis of local image brightness discontinuities AND Analysis of adjacent regions that support local gradient Only stable edges are returned Stability is defined as shape consistency of selected adjacent regions Edges are returned as linked coordinate lists (no post-processing is required) All steps are highly efficient Idea: find most stable nodes within component tree Calculation of stability value per node [2] Comparing a region at level N to its father region at level N−Δ Δ is stability parameter of method Stability criterion: Shape similarity between regions Shape similarity is measured using chamfer distance Chamfer distance ═ look-up of boundary distance transform values Partial (!) matches are returned Locally most stable nodes within component tree are selected Each selected node provides Partially matched region boundaries Saliency value Saliency value is the level of the region within the tree Canny [3]Berkeley [4]Our method PRFPRFPRF applelogos bottles giraffes mugs swans horses average Matlab CODE and more results available at Direct comparison to Canny (all edges with length < 50 were removed) Red: Canny and Green: Our method Input Image Inverted Gradient Magnitudes Component Tree Stability Analysis Linked Edge List Input Image Gradient Magnitudes Cross section level tCross section level t+1 Component Tree