IEEE Trans Pattern Anal Mach Intell - On Differential Photometric Reconstruction for Unknown, Isotropic BRDFs.

Tópicos

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Resumo

We present a comprehensive theory of photometric reconstruction from image derivatives, in the presence of a general, unknown isotropic BRDF. We derive precise topological classes up to which the surface may be determined and specify exact priors for a full geometric reconstruction. These results are the culmination of a series of fundamental observations. First, we exploit the linearity of differentiation to discover BRDF-independent photometric invariants. For the problem of shape from shading, we show that isocontours of constant magnitude of the gradient may be recovered. For the problem of photometric stereo, we derive a photometric flow that relates image derivatives to surface geometry, using just two measurements of spatial and temporal image derivatives from unknown light directions on a circle. The photometric flow is shown to determine the surface up to isocontours of constant magnitude of the surface gradient, as well as isocontours of constant depth. Further, we prove that specification of the surface normal at a single point completely determines the surface depth from these isocontours. Additionally, we propose practical algorithms that require initial or boundary information, but recover depth from lower order derivatives. Our theoretical results are illustrated with several examples on synthetic and real data.

Resumo Limpo

present comprehens theori photometr reconstruct imag deriv presenc general unknown isotrop brdf deriv precis topolog class surfac may determin specifi exact prior full geometr reconstruct result culmin seri fundament observ first exploit linear differenti discov brdfindepend photometr invari problem shape shade show isocontour constant magnitud gradient may recov problem photometr stereo deriv photometr flow relat imag deriv surfac geometri use just two measur spatial tempor imag deriv unknown light direct circl photometr flow shown determin surfac isocontour constant magnitud surfac gradient well isocontour constant depth prove specif surfac normal singl point complet determin surfac depth isocontour addit propos practic algorithm requir initi boundari inform recov depth lower order deriv theoret result illustr sever exampl synthet real data

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