ICPR 2026 · Accepted

SHARC : Reference Point Driven Spherical Harmonic Representation for Complex Shapes

A compact, fast, and genus-agnostic shape representation that encodes distance fields via optimally placed interior reference points and Spherical Harmonics.

Panagiotis Sapoutzoglou  ·  George Terzakis  ·  Maria Pateraki
National Technical University of Athens, Athens, Greece
Code arXiv
Shape Representation Spherical Harmonics 3D Reconstruction
Abstract

We propose SHARC, a novel framework that synthesizes arbitrary, genus-agnostic shapes by means of a collection of Spherical Harmonic (SH) representations of distance fields. These distance fields are anchored at optimally placed reference points in the interior volume of the surface in a way that maximizes learning of the finer details of the surface.

To achieve this, we employ a cost function that jointly maximizes sparsity and centrality in terms of positioning, as well as visibility of the surface from their location. For each selected reference point, we sample the visible distance field to the surface geometry via ray-casting and compute the SH coefficients using the Fast Spherical Harmonic Transform (FSHT).

To enhance geometric fidelity, we apply a configurable low-pass filter to the coefficients and refine the output using a local consistency constraint based on proximity. Evaluation of SHARC against state-of-the-art methods demonstrates that the proposed method outperforms existing approaches in both reconstruction accuracy and time efficiency without sacrificing model parsimony.

SHARC pipeline: From input mesh through candidate generation, visibility-aware anchor selection, SH distance field encoding, to reconstruction
Figure 1. SHARC Pipeline Overview — From a dense pool of interior candidates, we select a sparse set of reference points that maximize surface visibility. For each point, the local radial distance field is encoded into Spherical Harmonic (SH) coefficients. To reconstruct the shape, we decode these fields and recover the surface points, using a local consistency constraint to filter noisy reconstructed points.
Method

What Makes SHARC Different

⚡
Execution Speed

Both encoding and decoding stages are significantly faster than state-of-the-art. For instance, the Thai Statue (10M-face mesh) is encoded in just 8 seconds.

⚖️
Accuracy vs. Compactness

Strikes a balance between representation complexity (number of reference points + SH coefficients) and reconstruction quality, outperforming all baselines.

🔍
Proximity-Based Reconstruction

Omnidirectional distance fields per reference point, filtered by proximity. Nearest reference point wins — sharper, more accurate surfaces.

Results

Quantitative Comparison

Evaluated across PSB, Stanford, Thingi10k, and ShapeNet datasets. All metrics expressed as % of object diameter. \(|\mathcal{C}|\) represents the number of primitives, which for the case of Raw MA and CoverageAxis++ are the number of medial balls, for MASH anchor points, and for our case reference points. \(d_{\mathrm{CD}}\) is the Chamfer Distance, while \(\overrightarrow{\epsilon}, \overleftarrow{\epsilon}, \overleftrightarrow{\epsilon}\) represent the forward, backward, and symmetric Hausdorff distances, respectively.

121×
Compression vs. Raw MA
Thai Statue (181MB → 1.49MB)
~46
Mean Primitives on PSB
vs 200–400 for MASH
<20s
Encoding at \(|\mathcal{C}|=200\)
Nearly constant runtime
Method PSB Stanford Thingi10k
\(|\mathcal{C}|\) \(d_{\mathrm{CD}}\) \(\overrightarrow{\epsilon}\) \(\overleftarrow{\epsilon}\) \(\overleftrightarrow{\epsilon}\) \(|\mathcal{C}|\) \(d_{\mathrm{CD}}\) \(\overrightarrow{\epsilon}\) \(\overleftarrow{\epsilon}\) \(\overleftrightarrow{\epsilon}\) \(|\mathcal{C}|\) \(d_{\mathrm{CD}}\) \(\overrightarrow{\epsilon}\) \(\overleftarrow{\epsilon}\) \(\overleftrightarrow{\epsilon}\)
Raw MA 30k 0.56 2.43 2.25 2.46 83.7k 0.61 3.26 2.26 3.27 53.3k 2.23 7.34 6.84 7.42
CoverageAxis++ 310 0.62 2.86 2.20 2.87 510 0.74 3.30 2.46 3.37 654 1.59 5.53 5.26 5.83
MASH 200 0.31 1.02 1.53 1.64 400 0.38 1.39 1.33 1.49 400 0.52 1.77 2.74 2.99
SHARC (Ours) 46 0.28 0.73 0.62 0.74 77 0.33 1.07 0.89 1.08 118 0.39 1.72 1.28 1.78

Best results highlighted. Metrics as % of diameter. SHARC achieves best \(d_{\mathrm{CD}}\) across all datasets with fewest primitives.

Category Ours Mash Coverageaxis++ Raw Ma
\(|\mathcal{C}|\) \(d_{\mathrm{CD}}\) \(\overrightarrow{\epsilon}\) \(\overleftarrow{\epsilon}\) \(\overleftrightarrow{\epsilon}\) \(|\mathcal{C}|\) \(d_{\mathrm{CD}}\) \(\overrightarrow{\epsilon}\) \(\overleftarrow{\epsilon}\) \(\overleftrightarrow{\epsilon}\) \(|\mathcal{C}|\) \(d_{\mathrm{CD}}\) \(\overrightarrow{\epsilon}\) \(\overleftarrow{\epsilon}\) \(\overleftrightarrow{\epsilon}\) \(|\mathcal{C}|\) \(d_{\mathrm{CD}}\) \(\overrightarrow{\epsilon}\) \(\overleftarrow{\epsilon}\) \(\overleftrightarrow{\epsilon}\)
Airplane 46 0.23 0.92 0.53 0.97 200 0.27 1.21 1.47 1.63 199 0.49 2.79 1.55 2.80 82k 0.30 0.90 0.58 0.91
Chair 99 0.35 0.83 0.89 1.02 200 0.46 1.47 2.67 2.72 200 0.72 3.49 2.34 3.52 83k 0.44 1.11 0.98 1.15
Lamp 59 0.28 2.37 0.75 2.60 200 0.34 1.51 2.14 2.33 167 0.54 3.79 1.63 3.87 71k 0.32 2.20 0.65 2.22
Sofa 116 0.36 0.86 1.06 1.19 200 0.43 1.63 1.96 2.16 200 0.79 4.41 2.61 4.41 85k 0.44 1.65 0.96 1.68

Quantitative comparison across four ShapeNet categories (Airplane, Chair, Lamp, Sofa). We evaluate 100 models per category. Best values are highlighted in bold.

Timings Breakdown across Datasets (seconds)
Preprocessing
Encoding
Decoding/Reconstruction

Mean execution time (in seconds) for CoverageAxis++ (CA++), Raw Medial Axis (RMA), MASH, and our method across four datasets. The total time is decomposed into Preprocessing (gray), Encoding (blue), and Decoding/Reconstruction (neon red).

Ablation Studies

Design Choices Validated

Proximity Threshold \(\tau_{\text{prox}}\)

Without a threshold (\(\tau_{\text{prox}} =\) None), the selection is driven purely by visibility, resulting in a sparse representation (\(|\mathcal{C}| = 31\) for Armadillo) that fails to capture fine details like the scales on the leg or facial creases. Our default setting (\(\tau_{\text{prox}} = 0.2\)) enforces locality, recovering these high-frequency features with a compact set of anchors (\(|\mathcal{C}| = 60\)). A strict threshold (\(\tau_{\text{prox}} = 0.05\)) results in an excessive number of reference points (\(|\mathcal{C}| = 830\)) without significant visual improvement.

Proximity Threshold Ablation
SH Bandwidth \(L\)

Lower bandwidths (\(L = 16, 32\)) result in overly smoothed geometry, failing to capture high-frequency features. Our default setting (\(L = 64\)) successfully recovers fine details such as the dragon’s scales and the sharp corners of the skyscrapers. Doubling the bandwidth to \(L = 128\) offers minor visual improvement while increasing the storage footprint.

SH Bandwidth Ablation
Lanczos Smoothing

Without applying a smoothing filter, the result exhibits significant ringing artifacts, visible as high-frequency ripples on the neck and body scales. Applying Lanczos smoothing effectively suppresses this noise, restoring a clean surface while preserving the underlying geometric structure.

Lanczos Smoothing Ablation
Scalability with \(|\mathcal{C}|\)

SHARC achieves lowest Chamfer Distance even at \(|\mathcal{C}|<50\), while maintaining near-constant runtime across all budgets.

Computation Time (s)
Chamfer Distance (10⁻³)
Citation

BibTeX

@article{sapoutzoglou2026sharc,
      title={SHARC: Reference point driven Spherical Harmonic Representation for Complex Shapes},
      author={Panagiotis Sapoutzoglou and George Terzakis and Maria Pateraki},
      year={2026},
      journal={arXiv:2604.01894}
    }