[Paper Review] Learning for Multi-Model and Multi-Type Fitting

Xun Xu, Loong‐Fah Cheong+1 more|arXiv (Cornell University)|Jan 29, 2019

Anomaly Detection Techniques and Applications58 references4 citations

TL;DR

This paper proposes a deep learning framework for multi-model and multi-type geometric fitting by learning clustering-friendly feature embeddings that maximize inter-cluster separation and minimize intra-cluster variance. The method uses a supervised contrastive loss (MIMI) to train a network to embed data points such that K-means clustering on the features enables accurate model fitting and automatic model selection, achieving state-of-the-art performance on synthetic and real-world multi-type fitting tasks with minimal hyperparameter tuning.

ABSTRACT

Multi-model fitting has been extensively studied from the random sampling and clustering perspectives. Most assume that only a single type/class of model is present and their generalizations to fitting multiple types of models/structures simultaneously are non-trivial. The inherent challenges include choice of types and numbers of models, sampling imbalance and parameter tuning, all of which render conventional approaches ineffective. In this work, we formulate the multi-model multi-type fitting problem as one of learning deep feature embedding that is clustering-friendly. In other words, points of the same clusters are embedded closer together through the network. For inference, we apply K-means to cluster the data in the embedded feature space and model selection is enabled by analyzing the K-means residuals. Experiments are carried out on both synthetic and real world multi-type fitting datasets, producing state-of-the-art results. Comparisons are also made on single-type multi-model fitting tasks with promising results as well.

Motivation & Objective

• To address the challenge of fitting multiple geometric models of different types (e.g., lines, circles, homographies) simultaneously in the presence of noise and sampling imbalance.
• To eliminate the need for manual parameter tuning in model fitting by learning data-driven feature representations that are inherently clustering-friendly.
• To enable automatic model selection (i.e., determining the number of clusters/models) through residual analysis of K-means clustering in the embedded feature space.
• To overcome limitations of conventional RANSAC-style and subspace clustering methods in handling mixed-type models and high-dimensional, overlapping subspaces.
• To develop a unified framework that generalizes to both multi-model (same type, multiple instances) and multi-type (mixed model classes) fitting scenarios.

Proposed method

• The method trains a deep neural network using a novel MIMI loss that maximizes inter-cluster distance and minimizes intra-cluster variance in the feature space.
• The backbone network, CorresNet, processes non-grid data (e.g., point correspondences) and outputs a learned embedding of dimension d, with d chosen to match the maximum expected number of clusters.
• Inference is performed by applying K-means clustering to the network’s output embeddings, which group points of the same model type together.
• Model selection is achieved via simple, parameter-free heuristics such as Second Order Difference (SOD) and Silhouette Analysis applied to the K-means residuals.
• The MIMI loss is trained in a supervised manner using labeled inliers and outliers, with fixed cluster assignments during training to stabilize optimization.
• The framework is evaluated on synthetic data and real datasets like KT3DMoSeg, demonstrating robustness to sampling imbalance and model type ambiguity.

Experimental results

Research questions

• RQ1 Can a deep neural network learn feature embeddings that are inherently clustering-friendly for multi-model and multi-type geometric fitting?
• RQ2 Can the proposed method automatically determine the number of models (i.e., perform model selection) without relying on complex hyperparameter tuning?
• RQ3 How does the network perform on mixed-type fitting tasks where model types are ambiguous or overlapping (e.g., lines, circles, ellipses)?
• RQ4 Does the MIMI loss outperform ablations that only optimize for inter-cluster separation or intra-cluster compactness?
• RQ5 Can the method generalize to both multi-model (same type, multiple instances) and multi-type (mixed types) scenarios with consistent performance?

Key findings

• The proposed method achieves a mean classification error of 7.36% and a correct rate of 86.36% on model selection for the KT3DMoSeg dataset, outperforming SOD and Silhouette on other baselines.
• The MIMI loss consistently outperforms ablations (MaxInter, MinIntra, K-means loss) in terms of clustering error, demonstrating the necessity of jointly optimizing inter- and intra-cluster objectives.
• The optimal embedding dimension is found to be between 5 and 6, which aligns with the maximum number of clusters in each task, suggesting this as a practical heuristic.
• The method shows stable performance across embedding dimensions from 4 to 7, indicating robustness to hyperparameter choice.
• Feature visualization via T-SNE confirms that the learned embeddings group points by motion type (e.g., affine, homography) regardless of model type, even when the underlying geometry is ambiguous.
• The method achieves state-of-the-art results on both synthetic multi-type fitting and real-world multi-model fitting tasks, with minimal sensitivity to parameter tuning.