Computer Analysis of Regular Repetitive Textures

Regular rcpttitive texam arc common in rcal-workl scaux, occurring in both n a n d and man-made environments. Their analysis is important for image segmentatim and fos shape recovery from surf= texture. There are two fundamental problems in analyzing reguiar repetitive texture. F d y , rbc frcsucncy interpretation of any regular t e x m is ambiguous since that arc many altanative imqmatiap tbatccmspmd to the same texture. Secondiy, the v a y definition of regular repetition is c i m h since the elanencard the repetitive hzquency are defined in tamsof each otber. In this papa, we address tbcsc t w o p o b l a n s a n d ~ a n a u s w c r to each. To address the ambiguity of finqpmcy htmpmaa 'on we p~lll to the lattice theory and choose sucassiivc minima as the most fpndamental fnquaq vccuxs of the t~topre. To deal with thedcfidkm OfregularnpetitiOn, we compare t h e S t C U C t U d ~ topnmimtntfcaMesinthe~Tbesttbearmcal concepsarehrporatcdintoa working systrm, capable of d y z i a g and scgmauing regular repshive tcxtlacs in real-world images. In contrast with pevioruwark, ora tcchniqueinvolv csentirely localanalysisaadistherebyrobusttotcxture distonion. Regular repetitive exaxes are CQI~IIY)EI in real-worfd scenes. Tbey occur both as arcSulL of natural pmcesses (e-g. the repetitive mom of reptile skin) and the eff.m of man (eg. man's aukiag of a city scc11c). Understanding these textures is imponam not only as abasis for image SCgmGntation butaiso because regular repetitive textures can provi&valuabIcinfonnationfor~gsrtrfactopieatatioa A fundamental problem in analyzing regular textures, howeva, is that the &finition of regular repetitive texture is circular. The fnsoencr of the texture is Mined as the spatial dispiacancnt becwccn elantnts of the texture. but the element of the texture is defined as that portion of the image that is ngulariy rcpeatcd This circular dependency is usually handXed by obtaining information about the reptitivc iiesuenCy without considaing the natllre of the texture element or vice vasa. In both applloaches a global adysis of the textme is pufkxmcd, restricting the applicability oftheaIglxithstoundistoro#i samplesdasin@crepetitivetcxture In comas to these approaches, omwurkanploys apmdyfocalaaaiysis toidentify tbe repetitive structure of the m o s ~ (&minant) fin nsplarnqeitive ocrmres i n d d images. In this way, we identify the resnlarnpecitive=hti-m * between textme elemenowithoatirtntifvinp the texMeeianeau themselves. A second problem in aaaIyzing regular repetitive textmw is that: cvtll whea we know the locations of textw eluxmts, tbue are many alternative pairs of fhqwncy vccmrs hat equally dcscribc the pattcnr of the texture