MultiLink: Multi-class Structure Recovery via Agglomerative Clustering and Model Selection

TL;DR

MultiLink tackles multi-class structure recovery under noise and outliers by unifying preference analysis with agglomerative clustering and on-the-fly model selection across non-nested model classes $\{\,\Theta_k\}\_{k=1}^K$. It builds a single, multi-class preference embedding from a pooled hypothesis set $\mathcal{H}=\bigcup_k H_k$ and uses single-linkage clustering; two clusters $U,V$ merge only if there exists $\hat{k}$ with $g_{\hat{k}}(U\cup V) \le g_k(U) + g_k(V)$, where $g_k(\cdot)$ is the Gric cost for class $\Theta_k$. By fitting models on-the-fly during merges and integrating Gric-based model selection into the clustering, MultiLink is robust to outliers, less sensitive to the inlier threshold $\varepsilon$, and capable of recovering non-nested, mixed-model structures faster than prior preference-based methods. The approach yields accurate results on 2D fitting, two-view relations, and video motion segmentation, with substantial stability across varying data conditions, and is complemented by publicly available code for practitioners.

Abstract

We address the problem of recovering multiple structures of different classes in a dataset contaminated by noise and outliers. In particular, we consider geometric structures defined by a mixture of underlying parametric models (e.g. planes and cylinders, homographies and fundamental matrices), and we tackle the robust fitting problem by preference analysis and clustering. We present a new algorithm, termed MultiLink, that simultaneously deals with multiple classes of models. MultiLink combines on-the-fly model fitting and model selection in a novel linkage scheme that determines whether two clusters are to be merged. The resulting method features many practical advantages with respect to methods based on preference analysis, being faster, less sensitive to the inlier threshold, and able to compensate limitations deriving from hypotheses sampling. Experiments on several public datasets demonstrate that Multi-Link favourably compares with state of the art alternatives, both in multi-class and single-class problems. Code is publicly made available for download.

Figures (7)

• Figure 1: An example of multi-class recovery. MultiLink extracts planes and cylinders from the input point cloud. Structure membership is color coded.
• Figure 2: MultiLink combines single-linkage clustering and Gric. Clusters are merged as long as the Gric score improves when fitting suitable models on-the-fly. Colors indicate how cluster aggregation proceeds in the dendrogram.
• Figure 3: Illustration of merge with Gric.
• Figure 4: Line fitting: MultiLink vs T-linkage. Fig. \ref{['fig:star5result']}: the worst result of MultiLink for $\varepsilon = 3\sigma$ over 50 trials. Figs. \ref{['fig:star5_me']} and \ref{['fig:star5_outlier']}: the median ME (solid line), IQR (shaded area), maxima ($+$) and minima ($\circ$) as a function of $\varepsilon$ and outlier ratio.
• Figure 5: Worst results by MultiLink on conic fitting.