NAISR: A 3D Neural Additive Model for Interpretable Shape Representation (2303.09234v5)

Abstract: Deep implicit functions (DIFs) have emerged as a powerful paradigm for many computer vision tasks such as 3D shape reconstruction, generation, registration, completion, editing, and understanding. However, given a set of 3D shapes with associated covariates there is at present no shape representation method which allows to precisely represent the shapes while capturing the individual dependencies on each covariate. Such a method would be of high utility to researchers to discover knowledge hidden in a population of shapes. For scientific shape discovery, we propose a 3D Neural Additive Model for Interpretable Shape Representation ($\texttt{NAISR}$) which describes individual shapes by deforming a shape atlas in accordance to the effect of disentangled covariates. Our approach captures shape population trends and allows for patient-specific predictions through shape transfer. $\texttt{NAISR}$ is the first approach to combine the benefits of deep implicit shape representations with an atlas deforming according to specified covariates. We evaluate $\texttt{NAISR}$ with respect to shape reconstruction, shape disentanglement, shape evolution, and shape transfer on three datasets: 1) $\textit{Starman}$, a simulated 2D shape dataset; 2) the ADNI hippocampus 3D shape dataset; and 3) a pediatric airway 3D shape dataset. Our experiments demonstrate that $\textit{Starman}$ achieves excellent shape reconstruction performance while retaining interpretability. Our code is available at $\href{https://github.com/uncbiag/NAISR}{https://github.com/uncbiag/NAISR}$.

• The paper introduces a novel 3D shape model that integrates deep implicit functions with covariate-specific deformations.
• It establishes an interpretable template approach that enables both individualized and population-level shape analysis.
• Empirical tests on simulated and clinical datasets demonstrate superior performance in shape reconstruction and analysis.

Insights into NAISR: A 3D Neural Additive Model for Interpretable Shape Representation

The paper "NAISR: A 3D Neural Additive Model for Interpretable Shape Representation," presented at the International Conference on Learning Representations (ICLR), introduces a novel approach to 3D shape representation leveraging the capabilities of deep implicit functions (DIFs). The proposed method, NAISR (Neural Additive Interpretable Shape Representation), addresses the challenge of representing 3D shapes with associated covariates, which is a gap in current shape representation methods, particularly those that aim to understand population-wide trends and patient-specific predictions.

Deep Implicit Function Paradigm

NAISR builds on the foundational framework of deep implicit functions (DIFs), which are widely accepted for their ability to efficiently encode 3D shapes as continuous functions with infinite resolution. DIFs have proven advantageous in tasks such as 3D shape reconstruction, generation, and editing. Prior work within this paradigm has not adequately addressed the nuanced representation of shapes that accounts for the influences of various covariates. NAISR fills this gap by incorporating covariate-specific deformations into the shape representation process.

Methodological Approach

NAISR uniquely combines DIFs with a shape atlas to yield a flexible yet interpretable shape representation model. This integration allows NAISR to model covariate effects at both individual and population levels through:

• Implicit Representation: Shapes are represented implicitly, facilitating adaptability to varying resolutions.
• Deformability: The model establishes point correspondences via displacement fields relative to a template shape, enabling the mapping and comparison of shapes.
• Disentanglement: Covariate-specific effects are disentangled to allow the composition of overall shape transformations.
• Evolution: The model is capable of evolving shape representations as covariates change, capturing temporal and geometric changes.
• Transferability: Changes can be applied to new shapes, predicting alterations such as anatomical developments or the outcomes of hypothetical interventions.

The methodology involves learning continuous deformable templates of 3D shapes represented by the zero level sets of signed distance functions. Covariate-induced deformations are aggregated to provide a composite transformation that approximates the target shape.

Empirical Validation

The authors validate NAISR using three datasets: a simulated 2D shape dataset (Starman), a 3D shape dataset from the Alzheimer's Disease Neuroimaging Initiative (ADNI), and a pediatric airway dataset. Quantitative metrics (Chamfer distance, Earth mover’s distance, and Hausdorff distance) highlight NAISR's superior performance in shape reconstruction over existing baseline models. Furthermore, NAISR’s interpretable nature is substantiated through visualizations of shape evolutions and transfers.

Implications and Future Directions

The implications of NAISR are both theoretical and practical. The model opens new avenues for interpretable shape analysis in computer vision, particularly in medical image analysis where understanding covariate effects is crucial. NAISR's ability to extrapolate shapes based on covariates may lead to insights into pathological developments and treatment outcomes, enabling applications in disease progression modeling and other domains requiring precise shape comprehension.

Future developments may focus on improving NAISR's robustness, particularly in handling complex and high-dimensional covariate spaces. An exploration of invertible transforms to ensure topology preservation in shape correspondences is also a promising trajectory. Moreover, integrating NAISR in real-world clinical applications to detect anomalies or predict patient-specific anatomical changes remains a vital endeavor for translating this research into impactful use cases.

By advancing neural shape representations into an interpretable domain, NAISR sets a significant precedent for the continued integration of machine learning in scientific discovery and medical applications.