# Multi-modal 3D Shape Reconstruction Under Calibration Uncertainty using Parametric Level Set Methods

## TL;DR

This paper introduces a robust, scalable 3D shape reconstruction method from multi-modal data that effectively handles calibration uncertainties using parametric level set techniques with ellipsoidal radial basis functions.

## Contribution

It presents a novel parametric level set approach that explicitly models calibration uncertainty, enabling accurate 3D reconstruction across diverse data modalities.

## Key findings

- Method accurately represents complex objects.
- Reconstruction is robust to measurement sparsity and noise.
- Effective across multiple data types like slices and silhouettes.

## Abstract

We consider the problem of 3D shape reconstruction from multi-modal data, given uncertain calibration parameters. Typically, 3D data modalities can be in diverse forms such as sparse point sets, volumetric slices, 2D photos and so on. To jointly process these data modalities, we exploit a parametric level set method that utilizes ellipsoidal radial basis functions. This method not only allows us to analytically and compactly represent the object, it also confers on us the ability to overcome calibration related noise that originates from inaccurate acquisition parameters. This essentially implicit regularization leads to a highly robust and scalable reconstruction, surpassing other traditional methods. In our results we first demonstrate the ability of the method to compactly represent complex objects. We then show that our reconstruction method is robust both to a small number of measurements and to noise in the acquisition parameters. Finally, we demonstrate our reconstruction abilities from diverse modalities such as volume slices obtained from liquid displacement (similar to CTscans and XRays), and visual measurements obtained from shape silhouettes.