Environmental Labelings in Low-Level Image Understanding

Abstract

In this paper we show how assumptions. andinfo rmati on conce rning _the extern al '":oriel propert1~s of " horiz onta l" an d "ve rti ca l" can ::ud m th e analys1s ofimages, even at the very lowest levels. of pro cessing. Y'l e derive severa l fund ame nt a l m at h ematica l r es ult s rcl at mgph enonwn a in both the gradient. space and the image space to the exte rn al world att ribut es ohori zo nt a l an d vertical. We thC'n show how these r es ults mte rr el ate three imag in g phenomena : the s urfa ces in the image , the exte rn al sensor r ~a r a m ete r s, and . t._he. env irOiu:n e nt a l l abl s. W e detail how, m general , spec 1f1 c mfo rm atw n r ega rdmg a ny_ two of these phPnoll?ena ca n be used to quantitativelyde nv e th e tlmd; occasiOnally ~me. ca n do . ev~n better . Algorithms for such quantJtat.Jve de nv atw ns are presented , including. two based on thHough _tr ansform . We furth er show how ce rt a m environme ntalperp endi c ul a rities ca n b e ex pl oited veryfficj e_ ntly , andeven elega ntly: ordinanly comp l ex math Slm))hf1es to th e extP nt that env ironm enta l dista nces ca n be ilirectly r ea_ d o ff th e im age. The power of such enviro nm enta l la bels IS th en demonstrated by a n an~lysiof the ~o ur ce. ofa mbiguit y in a simple illusion-h)( e 1m age conf1gur atw n. The paper conclud es with a n analysis of the class ofheuri st ics that have been invoked throughout . They a re seen to be in sta ntiati ons of the shape-from-t ext ur e m etaheuri st ics that "nea r implies preferred" and " pr efe rr ed impli es simple".