an edge. Such segmentation systems have characteristic failure modes: If cooperation runs amok, then all mech-anisms agree and the image is grayed-out, rather thansegmented. If such a failure occurs in an already seg-mented image, the image would appear to melt or fade. If competition is too strong, or cooperation too weak,then the image may fragment. For example, Terman and Wang's (1995) neural network (using nearest neighbor connectivity) tends to fragment images. Similarly, stere-opsis segmentation networks fragment images if thresh-olds for keeping cells active and/or entraining adjacentinactive cells are set too high (Marr, Palm, & Poggio,1978). Below, we examine situations (equiluminance andretinal stabilization) where percepts fade, melt, and/orfragment and argue these phenomena are understand-able in a segmentation/part-binding framework. These fading/fragmentation problems may be alleviated if mul-tiple segmentation networks share information aboutlocation of borders. Reinforcement between parallelnetworks—called ''cross-modal construction'' (Finkel& Edelman, 1989)—has the potential to reinforce andrefine estimates of image features (Roelfsema et al.,1996; Schillen & Ko ¨nig, 1994; Horn et al., 1991; Poggio, Gamble, & Little, 1988). Cross-modal construction is intuitive: Realistic segmentation networks have re-sponse thresholds; weak cooperative interactions be-tween segmentation networks responding to differentfeatures of the same image (e. g., chromatic and achro-matic form) allow the more active network to give theother network's units a boost above threshold, but donot entrain units not driven by sensory input, if theirthresholds are chosen appropriately (Horn et al., 1991). We argue that cross-modal construction depends on a stimulus-linked variant of the correlated noise that Horn used for synchronization. ORIGIN AND NATURE OF CROSSTALK-BASED CORRELATIONS BETWEEN ACHROMATIC AND CHROMATIC CORTICAL FORM MECHANISMS Retinogeniculate Origins of Correlations between Chromatic and Achromatic Mechanisms There is much evidence for chromatic/achromatic inter-actions in human vision (Mullen & Kingdom, 1991). Some interactions arise early in the visual pathway. About 80% of LGN cells have Type I receptive fields(center of different spectral sensitivity than its spatiallyopponent surround; Wiesel & Hubel, 1966); these P cellsrespond to both chromatic and achromatic stimuli (De Valois & Pease, 1971). P cells account for both the threshold chromatic and achromatic spatio-temporal contrast sensitivity functions (except for the achromaticlow spatial, high temporal frequency corner; Merigan &Maunsell, 1993; Kelly, 1983). Although the P cell's mixedsignal seems ambiguous, Ingling and Martinez's (1983,1985) algebraic identity factors the P cell's sensitivity into psychophysically meaningful terms. The expansion forr+g/C0cells (similar identities obtain for other cell types and for mixed cone surrounds; Billock, 1996) is: Prþg/C0¼RSe Te/C0GSi Ti ¼ð Rþ GÞfð Se/C0Si Þð Teþ Si Þþð Seþ Si Þð Te/C0Ti Þg=4 (Achromatic, Spatio-temporally bandpass) þð R/C0GÞfð Se/C0Si Þð Te/C0Ti Þþð Seþ Si Þð Teþ Ti Þg=4 (Chromatic, Spatio-temporally lowpass Þ Here, Rand Gare absorptions in L-and M-cones, Se,Si are center (excitatory) and surround (inhibitory) spatial weighting functions, and Te,Tiare center and surround temporal impulse response functions. Se,Si,Te,Tiare all lowpass functions of spatial/temporal frequency, so their sums are lowpass and differences are bandpass. A variation of Equation 2 models both the chromaticand achromatic contrast sensitivity functions (Burbeck& Kelly, 1980). For our current purposes, this formula-tion is unnecessarily complex; we develop some basicideas using a simplification and then return to thefull version when necessary. Temporarily neglectingtime gives Prþg/C0¼RCenter /C0GSurround ¼ð Rþ GÞð Se/C0Si Þ=2 (achromatic, bandpass tuning) þð R/C0GÞð Seþ Si Þ=2 (chromatic, lowpass tuning)ð3Þ For simplicity, we restrict space to one dimension ( x) and define the stimulus in terms of L and M coneabsorptions: Z(x)={ R(x),G(x)}. The response of the P cell to the stimulus is Prþg/C0ðx Þ/C10Zðx Þ¼0:5f Rðx Þþ Gðx Þg /C10 f Seðx Þ/C0Siðx Þg (Achromatic response) þ0:5f Rðx Þ/C0Gðx Þg /C10 f Seðx Þþ Siðx Þg (Chromatic response) where the convolution of two functions A(x)/C10B(x)=R A(t)B(x/C0t)dtand tis a dummy variable of in-tegration. Equations 3 and 4 reveal a subtle encoding of chromatic and achromatic information that is deci-pherable by cortical decoders. To see how, let theexcitatory center ( S e) and inhibitory surround ( Si) spatial weighting functions of this Type I cell be representedby Gaussians. The achromatic term is a difference of Gaussians that closely approximates a second spatialderivative of a Gaussian. The chromatic term is the sum of these Gaussians and is fit by a Gaussian with a space constant ( s) about 1. 83 times that of the achromatic term. If some simple assumptions (Billock, 1995) hold,(2) (4) 1038 Journal of Cognitive Neuroscience Volume 16, Number 6