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3D Morphable Models are models separating shape from appearance variation. Typically, they are used as a statistical prior in computer graphics and vision. Recent success with neural representations have caused a resurgence of interest in visual computing problems, leading to more accurate, higher fidelity, more expressive, and memory-efficient solutions. This report documents the program and the outcomes of Dagstuhl Seminar 22121, "3D Morphable Models and Beyond". This meeting of 39 researchers covered various topics, including 3D morphable models, implicit neural representations, physics-inspired approaches, and more. We summarise the discussions, presentations and results of this workshop.

Over the last decade, it has become increasingly affordable to digitize 2D and 3D shape information using multiple modalities, such as (video) cameras, image-based reconstruction systems, laser-range scanners, or depth cameras. If these dense models can be processed and described in an efficient and informative way, they can be used in applications, such as ergonomic design, virtual shopping, scientific and medical visualization, realistic simulation, photo-realistic rendering, the design of natural user interfaces, and semantic scene understanding. Traditionally, the notion of shape has been studied either by analyzing projections of shapes in images or by analyzing a sparse set of marker positions on 3D shapes. Typical tasks in 2D shape analysis include segmenting objects in images and tracking objects across a sequence of images, and typical tasks in 3D shape analysis include reconstructing the three-dimensional object depth from input images and identifying corresponding points on different 3D models. The analysis and processing of shape data becomes especially challenging because of the increasing amount of data captured by sensors used to acquire shapes, and because modern applications such as natural user interfaces require real-time processing of the input shapes. Meeting these challenges requires models of shape analysis that are compact and informative, thereby allowing the development of algorithms that can process large datasets efficiently. To achieve these goals, interdisciplinary approaches are needed that use concepts from a variety of research areas, including numerical computing, differential geometry, deformable shape modeling, sparse data representation, and machine learning. On the algorithmic side, many shape analysis tasks are modeled using partial differential equations, which can be solved using tools from the field of numerical computing. The fields of differential geometry and deformable shape modeling have recently begun to influence shape analysis methods. Furthermore, tools from the field of sparse representations, which aim to describe input data using a compressible representation with respect to a set of carefully selected basis elements, have the potential to significantly reduce the amount of data that needs to be processed in shape analysis tasks. The related field of machine learning offers similar potential. This seminar brought together 28 researchers from North America and Europe engaged in recent and upcoming developments in shape analysis who view these challenges from different perspectives and who together discussed the pressing open problems and novel solutions to them.