Shape Analysis

The design of furniture consists of two major components: geometric modeling and physical validity of shapes. While advances in software for 3D modeling have made it easier for even inexperienced users to design shapes and thus make content creation easy, there is a disconnect between the geometric design and the physical functionality assessment. The typical workflow for a designer is to create a 3D model followed by validation using a physical simulator, and depending on the validation results, the designer re-iterates the whole process. This is tantamount to trial-and-error, making it a slow process, not to mention (a) the lack of any feedback to the designer specific to why the design failed and (b) the inherent limited exploration of novel shapes by encouraging designers to opt for standard geometric shapes only. While there have been previous work on suggestive modeling and interactive shape exploration, these works are limited in their feedback such as providing only a binary response about whether the design is valid or not, lack of informed exploration, etc. This paper proposes “a computational design framework for efficient and intuitive exploration” of physically valid furniture design shapes. In particular, the framework allows constrained modeling of nail-jointed furniture design of furniture using medium density fiberboard, and is constrained on 3 conditions: connectivity, durability, and stability. The paper describes the proposed method and the theoretical justifications in explicit detail, and we provide a brief summary of the key details here. ...

The problem of shape manipulation is of interest to many domains, including but not limited to: image editing platforms, usage in real-time live performances, and enhancing graphical user interfaces. The goal of shape manipulation is to impart the ability to move and deform shapes in a manner that is akin to interacting with an object in the real world. Previous approaches to shape manipulation can be broadly categorized into (a) space-warp and (b) physics based techniques. ...

Given two shapes, $N$ samples are drawn from the edge elements of the shape. There are no specific constraints on these points - they can be either on the internal or the external contour of the object. Moreover, they also need not correspond to keypoints for the shape (such as maxima of curvature, inflection points, etc.), and although desired that the samples be uniform in spacing, this too is not a rigid criterion. ...

The authors propose using an implicit shape representation for the source and the target shapes. The Euclidean signed distance transform is used to model the shape of interest as the zero level set of a distance function. Let $\Phi: \Omega \to R^+$ denote the distance transform of a shape $S$. The shape defines a partition of the image domain $\Omega$ - the region enclosed by $S$ is denoted by $[R_S]$ and the background region is denoted by $[\Omega - R_S]$. Using signed Euclidean distance transform, we have ...

Introduction This paper presents an algorithm for generating statistical shape models by addressing it as a correspondence problem of finding the parameterization of each shape in the training set, instead of manually annotating a set of “landmark” points for each image in the training set. The authors demonstrate the robustness of the algorithm by applying it to a variety of training image sets - infarcts, kidneys, knee cartilages, hand outlines, hip prostheses, and left ventricles. The proposed minimum description length model leads to good compactness, specificity and generalizes well, outperforming the contemporary gold standard - manual landmarking. Moreover, the authors also show that this model can be extended to work with 3-D images. ...