The purpose of this study was to examine how discrete segments of contiguous space arising from perceptual or cognitive channels are mentally concatenated. We induced and measured errors in each channel separately, then summed the psychophysical functions to accurately predict pointing to a depth specified by both together. In Experiment 1, subjects drew a line to match the visible indentation of a probe into a compressible surface. Systematic perceptual errors were induced by manipulating surface stiffness. Subjects in Experiment 2 placed the probe against a rigid surface and viewed the depth of a hidden target below it from a remote image with a metric scale. This cognitively mediated depth judgment produces systematic under-estimation (Wu et al. in IEEE Trans Vis Comput Grap 11(6):684-693, 2005; confirmed here). In Experiment 3, subjects pointed to a target location detected by the indented probe and displayed remotely, requiring mental concatenation of the depth components. The model derived from the data indicated the errors in the components were passed through the integration process without additional systematic error. Experiment 4 further demonstrated that this error-free concatenation was intrinsically spatial, rather than numerical.
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