Appearance Compensation in Volume Rendering

arXiv:2610.15030v1 Announce Type: new Abstract: Can a volume that reproduces every external RGB view still have an incorrect density? We study this question in emission-absorption rendering with an independently parameterized, physically bounded effective source. Appearance compensates a density change by replacing the radiance that it removes from the rest of each ray. We characterize the surviving density information with a shared spatial appearance field. Our first result is an optimal density-only gain after finite-degree spherical-harmonic source refitting. A coupled tensor gauge and physical localized packets identify the sharp limiting nonlinear inverse coefficient as its reciprocal. Our second result realizes positive gain at every fixed finite degree for a residual set of isotropic spatial sources at one fixed density. At the same references, growing angular capacity hides a fixed nonzero density error while retaining physicality and any prescribed finite set of smoothness bounds. Local identifiability and the absence of a capacity-uniform recovery modulus therefore coexist. Our third result constructs an exact physical SH2 ambiguity: central density doubles and relative density L^2 error exceeds 14.52%, yet every external RGB ray is unchanged. We connect these continuum results to shared finite representations, continuous pixel measurements and density-sensitive acquisition. Complete-class certificates separate SH0, SH1 and SH2 fits at one learned density. Finite-camera results expose the distinct role of spatial capacity, and transmission measurements separate otherwise identical RGB fields. Controlled training tests and captured-smoke profiles supply mechanism evidence with explicit observation scopes. The results show why rendering accuracy alone cannot certify density: recovery also depends on appearance capacity, spatial resolution and measurement design.

Source: arXiv cs.CV | 2026-10-14

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