Compact Representation of Spectral BRDFs Using Fourier Transform and Spherical Harmonic Expansion

Abstract

This paper proposes a compact method to represent isotropic spectral BRDFs. In the first step, we perform a Fourier transform in the wavelength dimension. The resulting Fourier coefficients of the same order depend on three angles: the polar angle of the incident light, and the polar and azimuth angles of the outgoing light. In the second step, given an incident light angle, when the Fourier coefficients of the same order have an insensitive dependency on the outgoing direction, we represent these Fourier coefficients using a linear combination of spherical harmonics. Otherwise, we first decompose these Fourier coefficients into a smooth background that corresponds to diffuse component and a sharp lobe that corresponds to specular component. The smooth background is represented using a linear combination of spherical harmonics, and the sharp lobe using a Gaussian function. The representation errors are evaluated using spectral BRDFs obtained from measurement or generated from the Phong model. While maintaining sufficient accuracy, the proposed representation method has achieved data compression over a hundred of times. Examples of spectral rendering using the proposed method are also shown.

Recovery and representation of spectral bidirectional reflectance distribution function from an image‐based measurement system

“…The developed systems are high cost due to a long acquisition time and huge size of raw data as a common CCD image sensor needs multiple (12)(13)(14)(15)(16)(17)(18) exposures to extend its dynamic ranges for multispectral BRDF measurements. To overcome these limitations, Kim et al 5 developed a multispectral BRDF measurement system consisting of an LCTF and an HDR camera.…”

“…With the recent advances in computing power, the spectral-based methods have been actively researched in many areas: bidirectional reflectance distribution function (BRDF) measurements, 1-5 the characterization of multispectral imaging systems, [6][7][8][9] and representation based on the multispectral rendering pipeline. [10][11][12][13][14] Also, multispectral BRDF measurement systems [1][2][3][4][5] have been developed by using a liquid crystal tunable filter (LCTF) and a monochromatic image sensor. These systems acquire 17-33 spectral channels of BRDFs instead of the full spectral BRDF measurements but they are high cost and have a long acquisition time for measurements.…”

“…In contrast, a spectral‐based representation method can visualize the surface appearance of a given material in a physically correct way. With the recent advances in computing power, the spectral‐based methods have been actively researched in many areas: bidirectional reflectance distribution function (BRDF) measurements, the characterization of multispectral imaging systems, and representation based on the multispectral rendering pipeline …”

Efficient computations of scalable caustic rendering and reconstruction

“…Afterwards, progressive integration is done from one level to another level. Xu and Sun compress the surface BRDF by using Fourier transform and spherical harmonics [66]. Another approach is to minimize the spectral information by simplifying it while keeping the error to a minimum.…”

“…Our contribution in this aspect is that we analyse the index of refraction of the caustic object over the visible wavelengths and we cluster the wavelengths based on refraction direction similarities. In the implementation, our work process spectral information with 1 nm spacing instead of compressing the spectral information or using simpler representation as done by some of the previous work [63,64,65,66,67,68,69,70,71,72]. Our implementation is thus suitable for GPU as for each light ray we can do integration (i.e.…”