I M Avatar: Implicit Morphable Head Avatars from Videos (2112.07471v6)

Abstract: Traditional 3D morphable face models (3DMMs) provide fine-grained control over expression but cannot easily capture geometric and appearance details. Neural volumetric representations approach photorealism but are hard to animate and do not generalize well to unseen expressions. To tackle this problem, we propose IMavatar (Implicit Morphable avatar), a novel method for learning implicit head avatars from monocular videos. Inspired by the fine-grained control mechanisms afforded by conventional 3DMMs, we represent the expression- and pose- related deformations via learned blendshapes and skinning fields. These attributes are pose-independent and can be used to morph the canonical geometry and texture fields given novel expression and pose parameters. We employ ray marching and iterative root-finding to locate the canonical surface intersection for each pixel. A key contribution is our novel analytical gradient formulation that enables end-to-end training of IMavatars from videos. We show quantitatively and qualitatively that our method improves geometry and covers a more complete expression space compared to state-of-the-art methods.

• The paper presents an innovative framework that reconstructs accurate 3D head geometry from video data using implicit representations.
• It employs expression blendshapes, linear blend skinning weights, and pose correctives to align deformed and canonical spaces effectively.
• The method integrates a robust equality constraint and occupancy mapping to boost realism in facial animations and optimize rendering efficiency.

Analyzing the Representational Approach to Surface Intersection in Deformed and Canonical Spaces

This paper presents a comprehensive framework for understanding the complex relationships between deformed and canonical spaces in the context of surface intersections. Through the meticulous delineation of variables and functions, the paper offers an insightful discourse on managing these transformations effectively using mathematical representations and computational methodologies.

At the crux of this research are several essential variables and parameters that facilitate the paper of surface deformations and the interplay between canonical correspondences. The paper considers sampled deformed points ($x_d^i$) and their canonical correspondences ($x_c^i$), while also taking into account the intersections of surfaces in both deformed and canonical spaces ($x_d$ and $x_c$, respectively).

The paper leverages expression blendshapes ($\mathcal{E}$) and Linear Blend Skinning (LBS) weights ($\mathcal{W}$) alongside pose correctives ($\mathcal{P}$) to model expressions and deformations. These elements are evaluated at specific pixel locations ($p$) to understand visual output through a projection matrix $P(\cdot)$, which offers a spatial representation of these variable transformations on a 2D plane, mimicking camera or viewport projections.

Key relationships are regulated by a set of bone transformations ($T$) and expression parameters ($\psi$), which are employed to manipulate the physical model and drive the interaction between the measured and calculated points. A sophisticated equality constraint function $F$, with associated learnable parameters $\sigma_F$, serves as the principal computational model to maintain or enforce specified conditions during transformations.

A significant focus of the paper is on occupancy ($occ$), which is vital for determining the presence or alignment of surface points within a space. This concept is crucial in fields such as computer graphics and computational geometry, where correctly identifying and manipulating spatial intersections can influence rendering outcomes and model fidelity.

From a practical viewpoint, the framework can potentially be applied to advancements in facial recognition technologies, animation, and real-time rendering in virtual reality systems. By accurately parameterizing and predicting deformations, the methods proposed could significantly enhance the realism and computational efficiency of animated models.

The theoretical implications of this research highlight the necessity of robust algorithms capable of adapting to multidimensional transformations. The dynamic and parameter-intensive approach provides a promising pathway for future developments in AI-driven modeling techniques, with the potential to extend beyond static surface intersection challenges to more complex, interactive environments.

Overall, this paper contributes to the ongoing dialogue in computational modeling, emphasizing detailed parameter manipulation as a critical factor in achieving precise and adaptable representations of surface deformations within both deformed and canonical spaces. This focus aligns with broader trends in artificial intelligence and machine learning research aimed at optimizing multivariate models for enhanced predictive power and operational performance.