Multiplicative Fourier Level of Detail

We develop a simple yet surprisingly effective implicit representing scheme called Multiplicative Fourier Level of Detail (MFLOD) motivated by the recent success of multiplicative filter network. Built on multi-resolution feature grid/volume (e.g., the sparse voxel octree), each level's feature is first modulated by a sinusoidal function and then element-wisely multiplied by a linear transformation of previous layer's representation in a layer-to-layer recursive manner, yielding the scale-aggregated encodings for a subsequent simple linear forward to get final output. In contrast to previous hybrid representations relying on interleaved multilevel fusion and nonlinear activation-based decoding, MFLOD could be elegantly characterized as a linear combination of sine basis functions with varying amplitude, frequency, and phase upon the learned multilevel features, thus offering great feasibility in Fourier analysis. Comprehensive experimental results on implicit neural representation learning tasks including image fitting, 3D shape representation, and neural radiance fields well demonstrate the superior quality and generalizability achieved by the proposed MFLOD scheme.