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arXiv · 2610.15030

Appearance Compensation in Volume Rendering

Jianghong Zhou
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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.

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Jianghong Zhou. 2026-10-10. Appearance Compensation in Volume Rendering. https://arxiv.org/abs/2610.15030

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