Complex Shapes Reconstructed from Data Noise with New Robust Fitting Technique

Researchers are increasingly challenged by the need to accurately reconstruct multiple instances of non-classical geometric models from noisy data. Zongliang Zhang, Shuxiang Li, and Xingwang Huang, all from Jimei University, alongside Zongyue Wang, address this problem with a novel multi-instance robust fitting method. Their work significantly extends existing robust fitting techniques, traditionally designed for simpler classical models, to encompass more complex forms such as spirals and free-form shapes. By formulating the task as an optimisation problem incorporating a new, threshold-free estimator and a meta-heuristic optimiser, the authors demonstrate a robust approach to handling outliers and achieving global optimisation, offering a valuable tool for applications requiring precise reconstruction of multiple, complex geometric instances.

Multi-instance reconstruction of complex geometric shapes from noisy data

Researchers have developed a new method for robustly reconstructing multiple instances of non-classical geometric models from noisy data, addressing a significant limitation in current fitting techniques. Most existing robust fitting methods are designed for classical models like lines, circles, and planes, but struggle with more complex shapes such as spiral curves, procedural character models, and free-form surfaces.
This work introduces a novel approach capable of handling these non-classical models, moving beyond the reconstruction of single instances to simultaneously identify multiple occurrences within a dataset. The core of this breakthrough lies in formulating the multi-instance fitting task as an optimisation problem comprising a novel estimator and an optimiser.

The newly proposed estimator, based on model-to-data error, effectively manages outliers without requiring a pre-defined error threshold, a common inconvenience in traditional methods. Because the estimator is non-differentiable, a meta-heuristic algorithm is employed as the optimiser to efficiently search for the global optimum solution.

This combination allows for accurate and robust reconstruction even in the presence of significant noise and complex geometries. Crucially, the research overcomes the limitations of previous approaches that struggled with overlapping instances of the same model. Existing estimators often counted overlapping regions multiple times, leading to inaccuracies.

The new estimator instead utilises the number of nearest data points to each model instance as a regulariser, effectively avoiding this double-counting issue and improving the accuracy of multi-instance fitting. Experimental results demonstrate the effectiveness of the method across a range of non-classical models, with the associated code publicly available for further research and application.

This advancement has implications for various fields including point cloud segmentation, image alignment, and even applications in procedural character modelling. By enabling the robust reconstruction of complex shapes from noisy data, this work opens new possibilities for automated analysis and modelling in diverse scientific and engineering domains. The ability to accurately identify and reconstruct multiple instances of non-classical models represents a significant step forward in geometric modelling and robust estimation techniques.

Model-to-data error estimation for robust multi-instance geometric fitting

A novel estimator based on model-to-data error forms the core of this work, addressing the challenge of robustly fitting multiple instances of non-classical geometric models from noisy data. The research directly tackles limitations in existing methods, which predominantly focus on single instances and struggle with models lacking easily defined minimal subsets for parameter estimation.

This study formulates the multi-instance fitting task as an optimisation problem, comprising both an estimator and an optimiser designed to work in concert. Specifically, the proposed estimator calculates error based on the distance from data points to the model, achieving robustness to outliers without requiring a pre-defined error threshold.

This contrasts with conventional data-to-model error approaches that necessitate setting a threshold to identify and exclude outliers, a process that can be both inconvenient and sensitive to noise. Because the resulting estimator is non-differentiable with respect to model parameters, a meta-heuristic algorithm was implemented as the optimiser to efficiently search for the global optimum within the solution space.

To avoid overcounting in overlapping regions between multiple model instances, the estimator utilises the number of nearest data points associated with each instance as a regulariser. This approach ensures that shared nearest neighbours are counted only once, improving the accuracy of multi-instance fitting.

The effectiveness of this methodology was demonstrated through experiments utilising various non-classical models, including procedural character models and Euler spirals, validating its ability to reconstruct multiple instances from noisy data. The complete implementation is publicly available to facilitate further research and application.

Multi-instance model reconstruction via nearest neighbour regularisation and error estimation

Researchers developed a novel estimator and optimizer for reconstructing multiple instances of non-classical models from noisy data. This work addresses limitations in existing robust fitting methods, which are largely designed for classical models like lines and circles or focus on single model instance reconstruction.

The proposed method formulates multi-instance fitting as an optimization problem, utilising an estimator based on model-to-data error that avoids the need for a predefined error threshold for outlier handling. The core of this approach lies in a new estimator designed to circumvent issues with overlapping regions when identifying multiple model instances.

Unlike previous methods that used model measure as a regularizer, leading to double-counting in overlapping areas, the current study employs the number of nearest data points of model instances as the regularizer. This technique effectively eliminates double-counting, allowing for more accurate multi-instance model fitting.

The estimator’s non-differentiability with respect to model parameters necessitated the use of a meta-heuristic algorithm as the optimizer to achieve a global optimum. This research successfully avoids the requirement of a predefined error threshold, a common inconvenience in data-to-model error approaches.

By utilising model-to-data error, the estimator inherently handles outliers without needing to establish a specific threshold value. The implementation of this method is publicly available, facilitating further research and application. The code repository can be accessed at https://github.com/zhangzongliang/fitting, enabling reproducibility and expansion of this work.

Robust multi-instance fitting via nearest point regularisation and meta-heuristic optimisation

A novel approach for the robust fitting of multiple instances of non-classical geometric models has been developed. Unlike traditional methods designed for simple shapes like lines and circles, this work addresses the challenges posed by complex models such as spirals and procedural characters. The core of this advancement is a new estimator, termed NPRE, which effectively handles overlapping instances and outliers without requiring a manually defined error threshold.

This method formulates the multi-instance fitting task as an optimisation problem, utilising the number of nearest data points as a regulariser within the NPRE estimator. This regularisation resolves the issue of double-counting instances sharing the same region, enhancing accuracy in reconstruction. A meta-heuristic optimisation algorithm was employed to refine the model parameters, enabling precise reconstruction of multiple geometric instances from noisy data across diverse datasets including synthetic data, procedural characters, and 3D highway curves.

The authors acknowledge limitations in computational efficiency, particularly when dealing with highly complex models or real-time applications. Future research will concentrate on improving the speed of the optimisation process to facilitate the handling of models with a greater number of parameters. This work establishes a foundation for robustly reconstructing complex geometric models from noisy data, potentially benefiting applications requiring accurate 3D reconstruction and scene understanding.