Abstract

Groucst is a global partitioning process that integrates local cu2 distribuOX over the entire image. We identify fou types of pairwise relationships, attraction and repuJY62O each of which can be symmetric or asymmetric. We represent these relationships with two directed graphs. We generalize the normalizedcur criteria to partitioning on directed graphs.Ou formurm24D resu4D in Rayleigh quigh2 ts on Hermitian matrices, where the real part describesuSX7DS2OS relationships, with positive nu bers for attraction, negative nu bers for repu66S2O and the imaginary part describes directed relationships. Globally optimalsoluDD7Y can be obtained by eigendecomposition. The eigenvectors characterize the optimal partitioning in the complex phase plane, with phase angle separation determining the partitioning of vertices and the relative phase advance indicating the ordering of partitions. WeuX directedrepud2x6 relationships to encode relative depthcut and demonstrate thatou method leads to simum2SxxS7 image segmentation and depth segregation. 1 Int1 duct43 Thegroupin problem emerges from several practicalapplication inplicat imagesegmen tation textantzM(( an dataminz(3 In its basic form, the problem conlemz ofextractin from a largen umber of data poin ts, i.e., pixels, wordsan documen ts, the overall organ(RM3zW structures thatcan be used to summarize the data. This allows on to makesen# of extremely large sets of data.In human perception this ability to group objectsan detectpattern is called perceptual organalzR#57 It has been clearlydemonzM94MR in various perceptual modalities such asvision audition an somatosen597zn [6]. Toun354zW3M thegroupin problem, wen(M toan( er two basicquestionR 1) what is the rightcriterion forgroupinR 2) how to achieve thecriterion computationzW33 ...

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