It has been a longstanding goal in computer vision to describe the 3D physical space in terms of parameterized volumetric models that would allow autonomous machines to understand and interact with their surroundings. Such models are typically motivated by human visual perception and aim to represents all elements of the physical word ranging from individual objects to complex scenes using a small set of parameters. One of the de facto stadards to approach this problem are superquadrics - volumetric models that define various 3D shape primitives and can be fitted to actual 3D data (either in the form of point clouds or range images). However, existing solutions to superquadric recovery involve costly iterative fitting procedures, which limit the applicability of such techniques in practice. To alleviate this problem, we explore in this paper the possibility to recover superquadrics from range images without time consuming iterative parameter estimation techniques by using contemporary deep-learning models, more specifically, convolutional neural networks (CNNs). We pose the superquadric recovery problem as a regression task and develop a CNN regressor that is able to estimate the parameters of a superquadric model from a given range image. We train the regressor on a large set of synthetic range images, each containing a single (unrotated) superquadric shape and evaluate the learned model in comparaitve experiments with the current state-of-the-art. Additionally, we also present a qualitative analysis involving a dataset of real-world objects. The results of our experiments show that the proposed regressor not only outperforms the existing state-of-the-art, but also ensures a 270x faster execution time.
Other researchers have tried to improve this method in various ways, for example in modifying the fitting function @cite_19 , or using multiresolution @cite_7 but still essentially relying on iterative methods of minimizing the fitting function. Instead of gradient least-squares minimization, other methods of minimization have also been tried, such as genetic algorithms @cite_8 . Several extensions of superquadrics were proposed in the literature @cite_25 @cite_0 , however, the basic superquadric shape model and the recovery method of Solina and Bajcsy prevailed in most applications of superquadrics, in particular for path and grasp planning in robotics, for modelling and interpretation of medical images etc. Later, Leonardis and Solina expanded Solina and Bajcsy's method to simultaneously deconstruct the input range image into several superquadrics, resulting in a perceptually relevant segmentation @cite_18 . Nevertheless, the procedure still relied on an iterative fitting procedure.
@cite_18 @cite_7 @cite_8 @cite_0 @cite_19 @cite_25
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We present an approach to reliable and efficient recovery of part-descriptions in terms of superquadric models from range data. We show that superquadrics can directly be recovered from unsegmented data, thus avoiding any presegmentation steps (e.g. in terms of surfaces). The approach is based on the recover-and-select paradigm. We present several experiments on real and synthetic range images, where we demonstrate the stability of the results with respect to viewpoint and noise. Rapidly acquiring the shape and pose information of unknown objects is an essential characteristic of modern robotic systems in order to perform efficient manipulation tasks. In this work, we present a framework for 3D geometric shape recovery and pose estimation from unorganized point cloud data. We propose a low latency multi-scale voxelization strategy that rapidly fits superquadrics to single view 3D point clouds. As a result, we are able to quickly and accurately estimate the shape and pose parameters of relevant objects in a scene. We evaluate our approach on two datasets of common household objects collected using Microsoft's Kinect sensor. We also compare our work to the state of the art and achieve comparable results in less computational time. Our experimental results demonstrate the efficacy of our approach. Supershape model is a recent primitive that represents numerous 3D shapes with several symmetry axes. The main interest of this model is its capability to reconstruct more complex shape than superquadric model with only one implicit equation. In this paper we propose a genetic algorithms to re-construct a point cloud using those primitives. We used the pseudo-Euclidean distance to introduce a threshold to handle real data imperfection and speed up the process. Simulations using our proposed fitness functions and a fitness function based on inside-outside function show that our fitness function based on the pseudo-Euclidean distance performs better. We present a new approach to the problem of modeling smoothly deformable shapes with convex polyhedral bounds. Our hyperquadric modeling primitives, which include superquadrics as a special case, can be viewed as hyperplanar slices of deformed hyperspheres. As the original hypersphere is deformed to its bounding hypercube, the slices undergo corresponding smooth deformations to convex polytopes. The possible shape classes include arbitrary convex polygons and polyhedra, as well as taperings and distortions that are not naturally included within the conventional superquadric framework. By generalizing Blinn's “blobby” approach to modeling complex objects, we construct single equations for nonconvex, composite shapes starting with our basic convex primitives. Hyperquadrics are of potential interest for the generation of synthetic images, for automated image interpretation and for psychological models of geometric shape representation, manipulation, and perception. A physically-based approach is presented to fitting complex 3D shapes using a novel class of dynamic models. These models can deform both locally and globally. The authors formulate deformable superquadrics which incorporate the global shape parameters of a conventional superellipsoid with the local degrees of freedom of a spline. The local global representational power of a deformable superquadric simultaneously satisfies the conflicting requirements of shape reconstruction and shape recognition. The model's six global deformational degrees of freedom capture gross shape features from visual data and provide salient part descriptors for efficient indexing into a database of stored models. Model fitting experiments involving 2D monocular image data and 3D range data are reported. >