Structure matters
Point clouds become more compressible when their physical or acquisition structure is made visible to the codec.
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3D data · Representation research · ZFP
Point-Cloud Compression
I investigated preconditioning techniques for 3D point clouds to improve their compressibility—starting with image-based representations and progressing to structure-aware ZFP experiments.
Point cloudsImage codingZFPLZ4LASzipExperimental evaluation
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00 / Interactive experiment
What happens when 3D coordinates are treated like image bytes?
This clean reproduction uses the 35,947-vertex Stanford Bunny. The original float32 XYZ payload is reshaped into an image-compatible byte layout, encoded, decoded, and rebuilt as a point cloud. Rotate the result to see how lossy image compression can leave shadows or aliases of the geometry.
Interactive representation experiment
See image coding alter a 3D point cloud.
Rotate the Stanford Bunny, compare the original XYZ cloud with the JPEG-decoded payload, and overlay both shapes to inspect geometric shadows and aliases.
Active view 00 · Original cloud 35,947 float32 XYZ points.
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PNG reconstructed this payload bit-for-bit. JPEG quality 100 changed 42.4% of payload bytes; its median XYZ error was 0.0617 in the source coordinate units.
01 / What I am investigating
Can representation engineering make irregular points easier to compress?
A point cloud is often stored as an unordered list of XYZ values. Generic compressors see neighbouring rows in memory, not neighbouring points in space. My work tests whether image layouts, ordering, spherical coordinates, compact indices, and controlled precision can expose enough structure for numerical compressors to become effective.
ReduceStorage and transmission load
PreserveUseful 3D geometry
AccountDecoder metadata and point order
ExplainWhere each saving actually comes from
02 / Research problem
A smaller stream is meaningful only when the decoded cloud remains useful.
LiDAR produces large spatial datasets for autonomous driving, mapping, digital twins, and robotics. Compression can reduce storage and network demand, but file size alone is an incomplete metric. A fair experiment must also measure geometric fidelity, attribute recovery, ordering requirements, decoder completeness, and runtime.
Change one representation decision
Each experiment isolates image layout, ordering, score, index coding, quantization, or numerical compression.
Count the recoverable result
Payload, framing, permutations, precision, reconstruction error, and decoder requirements are evaluated together.
03 / Method 1
Image-based byte wrapping: a deliberately simple first probe.
Image codecs may find byte-level repetition
If XYZ bytes are reshaped into an image carrier, PNG or JPEG may exploit local patterns even without understanding geometry.
PCD → image-compatible bytes → image codec → PCD
The binary XYZ payload is reshaped into an image-compatible byte layout. PNG is tested losslessly; JPEG quality 100 is tested as an explicitly lossy control.
Compare bytes and rebuild the cloud
Image wrapping reduced the stored payload by 10.71% with PNG and 3.93% with JPEG q100. The clean Bunny reproduction then exposes the reconstruction consequences.
Image wrapping reduced the stored payload
What this shows. PNG found more byte-level redundancy than JPEG q100, while the interactive Bunny makes the geometric cost of the lossy path visible.
04 / Method 2
Order-aware preconditioning: sorting has a hidden recovery cost.
Place similar values together
Sorting by radial distance or a structural score should make neighbouring numerical values easier for compression codecs to encode.
Compress payload and permutation
Original-order, distance-sorted, and score-sorted XYZ streams are compared. Sorted variants also store the permutation needed to restore point order.
A component improved; the archive did not
Sorting reduced the encoded range component by 18.22%, but complete order-recoverable controls became 28–38% larger.
05 / Method 3
Score-guided probing: ask which points are easier to encode.
A structural score may stratify compressibility
Points ordered by a recovered log-cardinality score may reveal regions that a numerical codec encodes more efficiently.
Remove one point and recompress
All points, the lower-score half, and the higher-score half are evaluated along a controlled removal sequence with signed byte changes.
The score was informative, not sufficient
The higher-score half began at 1.02378 compressed/raw versus 1.04550 for the lower-score half, but neither stream became smaller than raw.
Higher-score points were easier for the codec, but still expanded
What this shows. The score separated easier and harder subsets, but both compressed-to-raw ratios remained above the 1.00 raw-size line.
The one-by-one recompression is a diagnostic probe rather than a practical codec because its cost grows roughly quadratically.
06 / Method 4
Iterative midpoint-delta coding: the strongest exact custom primitive.
Angle dictionaries create compact integer structure
Quantized spherical angles repeat. Replacing them with indices should expose smaller, more regular values.
Recenter, store magnitudes, pack signs
Phi and theta indices are repeatedly centred, converted to absolute deltas, and paired with explicit sign bits until four-bit magnitudes remain.
2.499 bytes per point with exact index recovery
The 447,784-byte result was 37.91% below the raw angle-mapping reference and the smallest of six self-contained angle encodings.
The iterative midpoint-delta representation was smallest
What this shows. The midpoint-delta and explicit-sign representation produced the lowest self-contained bytes per point among the six exact encodings.
Each iteration must preserve its centre and sign stream, so the comparison includes the representation metadata.
07 / Method 5
Quantized spherical hybrid: combine codecs by stream type.
No single codec must encode everything
Distances, angle dictionaries, index deltas, and signs have different statistical structure and can use different encoders.
Spherical coordinates + RLE + ZFP + LZ4
XYZ is quantized in spherical form; repeated distances are run-length coded; angle indices use the midpoint-delta transform; numerical and byte streams are encoded separately.
Separate quantization from coding gain
The order-free quantized set reached 479,569 bytes. Quantization contributed the larger first reduction; the custom coding stage added a second measurable reduction.
Quantization produced the larger saving; custom coding added another
What this shows. The move to controlled precision supplied the larger first reduction, and the stream-specific custom coding stage added a second measurable reduction.
The experiment reports the order-free quantized set so the effect of quantization and coding can be separated.
08 / Method 6
Direct reversible ZFP: the baseline that explains the research problem.
Test ZFP without preprocessing
If a raw XYZ matrix already contains sufficient numerical correlation, reversible ZFP should reduce it without a representation change.
Compress and verify bit-for-bit recovery
The 179,170 × 3 float64 coordinate matrix is compressed directly using reversible ZFP and decoded exactly.
The unordered matrix expanded by 21.60%
The 4.300 MB numerical payload became 5.229 MB. A rectangular array in memory was not equivalent to a smooth spatial field.
Direct ZFP on an unordered particle array
What this shows. The exact ZFP stream was 21.60% larger than the original numerical payload.
The result motivates the representation study: list order does not expose the smooth spatial neighbourhoods expected by a structured-array codec.
09 / Methods tried alongside
The broader experiment record supplied baselines, controls, and alternative directions.
LZ4 on raw and structured streams
Useful for fast byte and index streams, but raw binary PCD showed no meaningful gain.
LASzip / LAZ
A strong point-cloud-specific baseline that remained better in the aligned whole-cloud comparison.
Three 16-bit grayscale axes
Mapped X, Y, and Z into image channels; achieved large stored-size reductions with reconstruction caveats.
Draco
Produced compact geometry payloads and supplied a useful point-cloud-specific reference alongside the custom experiments.
FFT-filtered spherical distance
An exploratory branch combining spherical dictionaries with frequency filtering; end-to-end fidelity remained unresolved.
Local filtering and smoothing
Tested structure-aware lossy reductions, including local standard-deviation filtering and PMLS-like smoothing.
Metropolis / LZF local search
Investigated ordering through iterative swaps; partial logs showed small gains but not a complete reproducible codec.
Fixed-width and packed index controls
Compared uint16, 10-bit, 20-bit-pair, normalized residual, and occurrence-list encodings against the custom transform.
Shannon entropy–based clustering
Grouped points by local information content to test whether entropy-homogeneous subsets exposed more regular, compressible structure.
Pseudogravitation
Explored attraction-inspired reordering to bring spatially related points into a more regular sequence before coding.
10 / Why it matters
Point-cloud compression remains an application-dependent systems problem.
Large 3D streams affect logging, mapping, remote robotics, simulation, and continuous model development. Current reference directions solve different parts of the problem rather than producing one universal winner.
MPEG G-PCC
Directly codes sparse 3D geometry and attributes. Its generality brings configuration, complexity, and rate–distortion choices.
MPEG V-PCC
Uses the video ecosystem for dynamic volumetric content, but projection and patch processing add artifacts and overhead.
Google Draco
Efficiently transports meshes and point clouds, while quantization and graphics-oriented assumptions must match the downstream task.
RIDDLE · Jiffy
Exploit acquisition order and temporal range-image structure, which is powerful but sensor- and representation-dependent.
SCP
Uses spherical LiDAR structure with learned compression; model cost, deployment complexity, and domain transfer remain practical considerations.
ZFP
Excels on structured numerical fields, but unordered particle lists do not naturally supply the smooth neighbourhoods it expects.
Collective gap
No single method simultaneously optimizes sparse and dense geometry, attributes, temporal prediction, exact order, random access, streaming latency, bounded error, and downstream perception quality. The central engineering task is to match representation, fidelity budget, and access pattern to the application—and measure the complete recoverable system.