Robust Multi-view Registration of Point Sets with Laplacian Mixture Model

MATLAB implementation of our ACPR 2021 paper (Springer). Given several partially overlapping 3D point sets, we recover the rigid pose of each view so they align into a single model — robustly, under heavy noise and outliers.

Unlike Gaussian-mixture methods (L2, outlier-sensitive), we model each point with a Laplacian Mixture Model: its centers are the corresponding points in the other views. The heavy-tailed, sparsity-inducing L1 likelihood absorbs outliers without any extra uniform component. Parameters and transformations are solved by EM — an E-step that builds L1 nearest-neighbour correspondences, and an M-step that solves a per-view weighted least-absolute-value (WLAV) alignment with two interchangeable solvers:

• ADMM ('admm', default) — variable splitting, soft-thresholding + SVD; fast.
• LPA ('lpa') — exponential-map linearization → LP → interior point; most accurate.

Quick start

>> demo        % registers the 10 Bunny views, prints errors, shows the result

The demo produces two figures — the 3-D synthesized model (each view a distinct colour) and a cross-section through it. Switch solver at the top of demo.m.

3-D synthesized model	Cross section

On your own data:

addpath(genpath('src'));
% views{i} : 3 x Ni points of view i in a common (initial) frame
% Ts       : 4 x 4 x M initial transformations
% ns{i}    : createns(raw_view_i, 'NSMethod','kdtree', 'Distance','cityblock')
[Ts_est, info] = register_lmm(views, Ts, ns, struct('solver','admm'));

Scale. The Laplacian scale starts at b = 1, so keep coordinates roughly unit-scale (the demo divides the raw Bunny by 1000). Rotation is scale-invariant; translation simply rescales back.

Layout

demo.m                 end-to-end demo on the Stanford Bunny
data/bunny.mat         10 partial views (noise + outliers) + ground truth
src/register_lmm.m     main EM loop
src/solvers/           wlav_admm, wlav_lpa, wls_svd, l1_interior_point, cg_solve
src/utils/             pc_transform, inv_transform, skew, reg_error
src/vis/               build_aligned_model, cross_section

Requirements: MATLAB (tested on R2026a) + Statistics and Machine Learning Toolbox.

Citation

@InProceedings{zhang2022robust,
  author    = {Zhang, Jin and Zhao, Mingyang and Jiang, Xin and Yan, Dong-Ming},
  title     = {Robust Multi-view Registration of Point Sets with Laplacian Mixture Model},
  booktitle = {Pattern Recognition: 6th Asian Conference, ACPR 2021},
  year      = {2022},
  publisher = {Springer International Publishing},
  pages     = {547--561},
  isbn      = {978-3-031-02444-3}
}

Acknowledgements

The L1 interior point solver and conjugate gradient routine are adapted from l1-magic (Justin Romberg, Caltech). The Bunny data and evaluation setup follow the EMPMR reference implementation Macariaa/EMPMR; the model is from the Stanford 3D Scanning Repository.

Released under the MIT License — see LICENSE.