Fractal geometry, defined by self-similar patterns across scales, is crucial for understanding natural structures. This work addresses the fractal inverse problem, which involves extracting fractal codes from images t...
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Fractal geometry, defined by self-similar patterns across scales, is crucial for understanding natural structures. This work addresses the fractal inverse problem, which involves extracting fractal codes from images to explain these patterns and synthesize them at arbitrary finer scales. We introduce a novel algorithm that optimizes Iterated Function System parameters using a custom fractal generator combined with differentiable point splatting. By integrating both stochastic and gradient-based optimization techniques, our approach effectively navigates the complex energy landscapes typical of fractal inversion, ensuring robust performance and the ability to escape local minima. We demonstrate the method's effectiveness through comparisons with various fractal inversion techniques, highlighting its ability to recover high-quality fractal codes and perform extensive zoom-ins to reveal intricate patterns from just a single image.
3D point clouds stand as one of the prevalent representations for 3D data, offering the advantage of closely aligning with sensing technologies and providing an unbiased representation of a measured physical scene. Pr...
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3D point clouds stand as one of the prevalent representations for 3D data, offering the advantage of closely aligning with sensing technologies and providing an unbiased representation of a measured physical scene. Progressive compression is required for real-world applications operating on networked infrastructures with restricted or variable bandwidth. We contribute a novel approach that leverages a recursive binary space partition, where the partitioning planes are not necessarily axis-aligned and optimized via an entropy criterion. The planes are encoded via a novel adaptive quantization method combined with prediction. The input 3D point cloud is encoded as an interlaced stream of partitioning planes and number of points in the cells of the partition. Compared to previous work, the added value is an improved rate-distortion performance, especially for very low bitrates. The latter are critical for interactive navigation of large 3D point clouds on heterogeneous networked infrastructures.
Spherical harmonics are a favorable technique for 3D representation, employing a frequency-based approach through the spherical harmonic transform (SHT). Typically, SHT is performed using equiangular sampling grids. H...
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Spherical harmonics are a favorable technique for 3D representation, employing a frequency-based approach through the spherical harmonic transform (SHT). Typically, SHT is performed using equiangular sampling grids. However, these grids are non-uniform on spherical surfaces and exhibit local anisotropy, a common limitation in existing spherical harmonic decomposition methods. This paper proposes a 3D representation method using Fibonacci Spherical Harmonics (FSH3D). We introduce a spherical Fibonacci grid (SFG), which is more uniform than equiangular grids for SHT in the frequency domain. Our method employs analytical weights for SHT on SFG, effectively assigning sampling errors to spherical harmonic degrees higher than the recovered band-limited function. This provides a novel solution for spherical harmonic transformation on non-equiangular grids. The key advantages of our FSH3D method include: 1) With the same number of sampling points, SFG captures more features without bias compared to equiangular grids;2) The root mean square error of 32-degree spherical harmonic coefficients is reduced by approximately 34.6% for SFG compared to equiangular grids;and 3) FSH3D offers more stable frequency domain representations, especially for rotating functions. FSH3D enhances the stability of frequency domain representations under rotational transformations. Its application in 3D shape reconstruction and 3D shape classification results in more accurate and robust representations. Our code is publicly available at .
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