Multi-instance robust fitting for non-classical geometric models

TL;DR

This work tackles robust, multi-instance fitting for non-classical geometric models from noisy data, where minimal subsets do not exist. It introduces the Nearest data Points Regularized estimator (NPRe), defining $\xi(M,D) = \left(\frac{|A(M,D)|}{|D|}\right)^{\lambda} \frac{\delta_D}{s(M,D)}$ to regularize model-to-data error without overlap counting, and uses a Cuckoo Search optimizer to handle the non-differentiable objective. The problem is formulated as maximizing $\xi$ over the union of $k$ model instances, solved sequentially for each instance. Empirical results on line fitting, procedural character fitting, and 3D road-curve reconstruction demonstrate accurate recovery of multiple non-classical structures from noisy data, with code available for reproduction. This approach holds potential for robust geometry reconstruction in vision, graphics, and GIS-like applications where non-classical models are common.

Abstract

Most existing robust fitting methods are designed for classical models, such as lines, circles, and planes. In contrast, fewer methods have been developed to robustly handle non-classical models, such as spiral curves, procedural character models, and free-form surfaces. Furthermore, existing methods primarily focus on reconstructing a single instance of a non-classical model. This paper aims to reconstruct multiple instances of non-classical models from noisy data. We formulate this multi-instance fitting task as an optimization problem, which comprises an estimator and an optimizer. Specifically, we propose a novel estimator based on the model-to-data error, capable of handling outliers without a predefined error threshold. Since the proposed estimator is non-differentiable with respect to the model parameters, we employ a meta-heuristic algorithm as the optimizer to seek the global optimum. The effectiveness of our method are demonstrated through experimental results on various non-classical models. The code is available at https://github.com/zhangzongliang/fitting.

Figures (6)

• Figure 1: Four examples of non-classical models. Each example is a procedural character model presented in lake2015human. A model consists of several strokes, which are represented by colored curves. The circled numbers indicate the starting positions of the strokes. A stroke may have sub-strokes, which are marked by white dots.
• Figure 2: An illustration of the overlapping issue. The blue and yellow dots represent data points. The green strips represent line segments (i.e., model instances). Let $M$ and $|M|$ denote a line segment and its length, respectively. In the figure, there are line segments $M_{12}$, $M_{34}$, $M_{36}$, and others. $|M_{12}|$ equals $|M_{45}|$. $|M_{34}|$ equals $|M_{56}|$. $|M_{34}|$ is also half of $|M_{12}|$. The model-to-data errors of each line segment are equal. For example, the $M_{12}$-to-data and $M_{34}$-to-data errors can be represented by the red arrow and the black arrow, respectively.
• Figure 3: Fitting on the noisy line data. The first row shows the data. The second row shows the results obtained by the state-of-the-art classical model fitting method xiao2024latent. The third row shows the results obtained by our method.
• Figure 4: Fitting on character data. \ref{['fig:character3:noisy']} Noisy image. \ref{['fig:character3:cs']} Results of fitting the character model on \ref{['fig:character3:noisy']}.
• Figure 5: Fitting on synthetic road curve data zhang20193d. \ref{['fig:circle-parabola:data']} the synthetic 3D point cloud data (white). \ref{['fig:circle-parabola:model']} The two road curves (red and green) reconstructed from \ref{['fig:circle-parabola:data']} by our method. \ref{['fig:circle-parabola:overlap']} The two reconstructed road curves (red and green) are shown together with the data (white).