You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
We propose to represent shapes as the deformation and combination of learnable elementary 3D structures, which are primitives resulting from training over a collection of shape. We demonstrate that the learned elementary 3D structures lead to clear improvements in 3D shape generation and matching. More precisely, we present two complementary approaches for learning elementary structures: (i) patch deformation learning and (ii) point translation learning. Both approaches can be extended to abstract structures of higher dimensions for improved results. We evaluate our method on two tasks: reconstructing ShapeNet objects and estimating dense correspondences between human scans (FAUST inter challenge). We show 16 improvement over surface deformation approaches for shape reconstruction and outperform FAUST inter challenge state of the art by 6 .

Cited Abstract(s):
[1]: Abstracting complex 3D shapes with parsimonious part-based representations has been a long standing goal in computer vision. This paper presents a learning-based solution to this problem which goes beyond the traditional 3D cuboid representation by exploiting superquadrics as atomic elements. We demonstrate that superquadrics lead to more expressive 3D scene parses while being easier to learn than 3D cuboid representations. Moreover, we provide an analytical solution to the Chamfer loss which avoids the need for computational expensive reinforcement learning or iterative prediction. Our model learns to parse 3D objects into consistent superquadric representations without supervision. Results on various ShapeNet categories as well as the SURREAL human body dataset demonstrate the flexibility of our model in capturing fine details and complex poses that could not have been modelled using cuboids.

[2]: The success of various applications including robotics, digital content creation, and visualization demand a structured and abstract representation of the 3D world from limited sensor data. Inspired by the nature of human perception of 3D shapes as a collection of simple parts, we explore such an abstract shape representation based on primitives. Given a single depth image of an object, we present 3DPRNN, a generative recurrent neural network that synthesizes multiple plausible shapes composed of a set of primitives. Our generative model encodes symmetry characteristics of common man-made objects, preserves long-range structural coherence, and describes objects of varying complexity with a compact representation. We also propose a method based on Gaussian Fields to generate a large scale dataset of primitive-based shape representations to train our network. We evaluate our approach on a wide range of examples and show that it outperforms nearest-neighbor based shape retrieval methods and is on-par with voxelbased generative models while using a significantly reduced parameter space.

[3]: We present a learning framework for abstracting complex shapes by learning to assemble objects using 3D volumetric primitives. In addition to generating simple and geometrically interpretable explanations of 3D objects, our framework also allows us to automatically discover and exploit consistent structure in the data. We demonstrate that using our method allows predicting shape representations which can be leveraged for obtaining a consistent parsing across the instances of a shape collection and constructing an interpretable shape similarity measure. We also examine applications for image-based prediction as well as shape manipulation.

[4]: Template 3D shapes are useful for many tasks in graphics and vision, including fitting observation data, analyzing shape collections, and transferring shape attributes. Because of the variety of geometry and topology of real-world shapes, previous methods generally use a library of hand-made templates. In this paper, we investigate learning a general shape template from data. To allow for widely varying geometry and topology, we choose an implicit surface representation based on composition of local shape elements. While long known to computer graphics, this representation has not yet been explored in the context of machine learning for vision. We show that structured implicit functions are suitable for learning and allow a network to smoothly and simultaneously fit multiple classes of shapes. The learned shape template supports applications such as shape exploration, correspondence, abstraction, interpolation, and semantic segmentation from an RGB image.

[5]: We present a learning framework for recovering the 3D shape, camera, and texture of an object from a single image. The shape is represented as a deformable 3D mesh model of an object category where a shape is parameterized by a learned mean shape and per-instance predicted deformation. Our approach allows leveraging an annotated image collection for training, where the deformable model and the 3D prediction mechanism are learned without relying on ground-truth 3D or multi-view supervision. Our representation enables us to go beyond existing 3D prediction approaches by incorporating texture inference as prediction of an image in a canonical appearance space. Additionally, we show that semantic keypoints can be easily associated with the predicted shapes. We present qualitative and quantitative results of our approach on CUB and PASCAL3D datasets and show that we can learn to predict diverse shapes and textures across objects using only annotated image collections. The project website can be found at https: akanazawa.github.io cmr .
Learning-based techniques offer a promising alternative to hand-crafted heuristics. Zhu al [2] use a Recurent Neural Network supervised by a traditional heuristic-based algorithm for cuboid fitting. Tulsiani al [3] use reconstruction loss to predict parameters of the cuboids that approximate an input shape, and thus do not require any direct supervision. Several recent techniques, concurrent to our work, extend this approach by using more complex primitives that can better approximate the surface, such as anisotropic 3D Gaussians [4] , categorie specifique morphable model [5] or superquadrics [1] . All of these techniques use a collection of simple hand-picked parametric primitives. In contrast, we propose to learn a set of deformable primitives that best approximate a collection of shapes.