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Multigrid

Point clouds and 3D

LiDAR, meshes, registration and depth — representations where the choice of format decides what you can compute.

A point cloud is a set, not an array. There is no first point, no neighbouring cell, no guaranteed spacing, and usually no guarantee that two scans of the same wall contain a single point in common. Almost every difficulty in this field comes from that one property. Convolution assumes a grid, so it has to be given one; nearest-neighbour search assumes an index, so one has to be built; alignment assumes correspondences, so they have to be guessed and then re-guessed. The algorithms with names — ICP, RANSAC, Poisson reconstruction, voxel pooling — are each a specific answer to “what do I do with an unordered set of coordinates?”

These pages work from the representation outward. Pick a voxel grid and you inherit a memory bill that grows with the cube of resolution; keep raw points and you inherit a neighbourhood query on every operation; write to the wrong file format and you can lose classification codes, GPS time, or six centimetres of coordinate precision without a single error being raised. Where a number appears here it is either taken from a published specification, named and linked, or derived on the page from assumptions stated in the sentence that uses them.

Point Cloud Classification Explained

Why a network that reads an unordered set has to be built out of a symmetric function, and what max pooling over points actually keeps.

9 min read

3D Object Detection From LiDAR Point Clouds

How a sparse sweep becomes oriented 3D boxes: the voxelisation step, what fraction of the grid is actually occupied, and why range destroys recall.

10 min read

Point Cloud Segmentation Explained

What changes when the label moves from the whole cloud to every point: the receptive-field problem, boundary error, and why mIoU replaced accuracy.

9 min read

Structure From Motion: Building 3D From a Set of Photos

How unordered photographs become camera poses and a sparse point cloud, and why depth precision degrades with the square of distance.

10 min read

3D Mesh Reconstruction From Images

The classical route from photographs to a watertight surface — dense stereo, oriented normals, Poisson reconstruction — and where each stage silently invents geometry.

10 min read

Point Cloud Registration and Alignment Explained

How ICP finds the rigid transform between two overlapping scans, worked through the SVD step by hand, and why it needs a good initial guess.

11 min read

Voxel Grids and Point Clouds: Why the Representation You Pick Changes the Model

The memory arithmetic of the same scene stored two ways, why occupancy falls as you refine the grid, and what each representation makes computable.

9 min read

Estimating Depth From a Single Image

Why single-image depth is formally unsolvable, which pictorial cues a model exploits instead, and what an affine-invariant output can and cannot be used for.

10 min read

Point Cloud Compression: What Gets Traded Away

Storage arithmetic for a large survey archive under lossless and octree coding, and exactly which properties each method destroys.

10 min read

Fusing LiDAR and Camera Data for Perception

The coordinate transform that puts a LiDAR point on a pixel, worked end to end, plus the calibration and timing errors that make it wrong.

10 min read

3D Model Embeddings for Shape Similarity Search

How a mesh or scan becomes a vector you can index, the two families of encoder, and the invariances you have to choose deliberately.

9 min read

SLAM Explained: How a Robot Builds a Map While Finding Itself in It

The circular dependency at the centre of SLAM, a worked information-weighted pose update, and why loop closure is both the fix and the biggest risk.

10 min read

Point Cloud Density and Scan Resolution Trade-offs

Point spacing derived from angular step and range, file size and scan time at three settings, and the physical limit that makes the finest setting pointless.

9 min read

Building a Digital Twin From a 3D Scan

The geometry-capture-to-model pipeline, the error budget that accumulates across setups, and why a scan-derived twin is a dated record rather than a live one.

10 min read

What Processing a LiDAR Point Cloud Actually Costs

Compute, storage, egress and human time derived from a stated daily point volume — and which of the four actually dominates.

10 min read

Ground Plane Removal in Point Cloud Data

A runnable RANSAC plane-fitting script that separates ground from everything else, with the plane arithmetic worked by hand and the guards that stop it fitting a wall.

10 min read

Converting Between Point Cloud File Formats (LAS, PLY, PCD)

The errors you get converting between LAS, PLY and PCD, what each format can and cannot hold, and the float32 precision trap that loses half a metre silently.

11 min read

Detecting a Sparse or Noisy Region in a Point Cloud Before Processing

Tracing an invented surface in a reconstruction back to the sparse region that caused it, and the density gate that catches it before the expensive stage runs.

10 min read

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