GPGPU implementation of growing neural gas: application to 3D scene reconstruction

Self-organising neural models have the ability to provide a good representation of the input space. In particular the Growing Neural Gas (GNG) is a suitable model because of its flexibility, rapid adaptation and excellent quality of representation. However, this type of learning is time-consuming, especially for high-dimensional input data. Since real applications often work under time constraints, it is necessary to adapt the learning process in order to complete it in a predefined time. This paper proposes a Graphics Processing Unit (GPU) parallel implementation of the GNG with Compute Unified Device Architecture (CUDA). In contrast to existing algorithms, the proposed GPU implementation allows the acceleration of the learning process keeping a good quality of representation. Comparative experiments using iterative, parallel and hybrid implementations are carried out to demonstrate the effectiveness of CUDA implementation. The results show that GNG learning with the proposed implementation achieves a speed-up of 6× compared with the single-threaded CPU implementation. GPU implementation has also been applied to a real application with time constraints: acceleration of 3D scene reconstruction for egomotion, in order to validate the proposal.

Growing Neural Gas approach for obtaining homogeneous maps by restricting the insertion of new nodes

The Growing Neural Gas model is used widely in artificial neural networks. However, its application is limited in some contexts by the proliferation of nodes in dense areas of the input space. In this study, we introduce some modifications to address this problem by imposing three restrictions on the insertion of new nodes. Each restriction aims to maintain the homogeneous values of selected criteria. One criterion is related to the square error of classification and an alternative approach is proposed for avoiding additional computational costs. Three parameters are added that allow the regulation of the restriction criteria. The resulting algorithm allows models to be obtained that suit specific needs by specifying meaningful parameters.

Combining visual features and Growing Neural Gas networks for robotic 3D SLAM

The use of 3D data in mobile robotics provides valuable information about the robot’s environment. Traditionally, stereo cameras have been used as a low-cost 3D sensor. However, the lack of precision and texture for some surfaces suggests that the use of other 3D sensors could be more suitable. In this work, we examine the use of two sensors: an infrared SR4000 and a Kinect camera. We use a combination of 3D data obtained by these cameras, along with features obtained from 2D images acquired from these cameras, using a Growing Neural Gas (GNG) network applied to the 3D data. The goal is to obtain a robust egomotion technique. The GNG network is used to reduce the camera error. To calculate the egomotion, we test two methods for 3D registration. One is based on an iterative closest points algorithm, and the other employs random sample consensus. Finally, a simultaneous localization and mapping method is applied to the complete sequence to reduce the global error. The error from each sensor and the mapping results from the proposed method are examined.

3D-based reconstruction using growing neural gas landmark: application to rapid prototyping in shoe last manufacturing

Customizing shoe manufacturing is one of the great challenges in the footwear industry. It is a production model change where design adopts not only the main role, but also the main bottleneck. It is therefore necessary to accelerate this process by improving the accuracy of current methods. Rapid prototyping techniques are based on the reuse of manufactured footwear lasts so that they can be modified with CAD systems leading rapidly to new shoe models. In this work, we present a shoe last fast reconstruction method that fits current design and manufacturing processes. The method is based on the scanning of shoe last obtaining sections and establishing a fixed number of landmarks onto those sections to reconstruct the shoe last 3D surface. Automated landmark extraction is accomplished through the use of the self-organizing network, the growing neural gas (GNG), which is able to topographically map the low dimensionality of the network to the high dimensionality of the contour manifold without requiring a priori knowledge of the input space structure. Moreover, our GNG landmark method is tolerant to noise and eliminates outliers. Our method accelerates up to 12 times the surface reconstruction and filtering processes used by the current shoe last design software. The proposed method offers higher accuracy compared with methods with similar efficiency as voxel grid.

Improving 3D Keypoint Detection from Noisy Data Using Growing Neural Gas

3D sensors provides valuable information for mobile robotic tasks like scene classification or object recognition, but these sensors often produce noisy data that makes impossible applying classical keypoint detection and feature extraction techniques. Therefore, noise removal and downsampling have become essential steps in 3D data processing. In this work, we propose the use of a 3D filtering and down-sampling technique based on a Growing Neural Gas (GNG) network. GNG method is able to deal with outliers presents in the input data. These features allows to represent 3D spaces, obtaining an induced Delaunay Triangulation of the input space. Experiments show how the state-of-the-art keypoint detectors improve their performance using GNG output representation as input data. Descriptors extracted on improved keypoints perform better matching in robotics applications as 3D scene registration.

3D reconstruction of medical images from slices automatically landmarked with growing neural models

In this study, we utilise a novel approach to segment out the ventricular system in a series of high resolution T1-weighted MR images. We present a brain ventricles fast reconstruction method. The method is based on the processing of brain sections and establishing a fixed number of landmarks onto those sections to reconstruct the ventricles 3D surface. Automated landmark extraction is accomplished through the use of the self-organising network, the growing neural gas (GNG), which is able to topographically map the low dimensionality of the network to the high dimensionality of the contour manifold without requiring a priori knowledge of the input space structure. Moreover, our GNG landmark method is tolerant to noise and eliminates outliers. Our method accelerates the classical surface reconstruction and filtering processes. The proposed method offers higher accuracy compared to methods with similar efficiency as Voxel Grid.

3D model reconstruction using neural gas accelerated on GPU

In this work, we propose the use of the neural gas (NG), a neural network that uses an unsupervised Competitive Hebbian Learning (CHL) rule, to develop a reverse engineering process. This is a simple and accurate method to reconstruct objects from point clouds obtained from multiple overlapping views using low-cost sensors. In contrast to other methods that may need several stages that include downsampling, noise filtering and many other tasks, the NG automatically obtains the 3D model of the scanned objects. To demonstrate the validity of our proposal we tested our method with several models and performed a study of the neural network parameterization computing the quality of representation and also comparing results with other neural methods like growing neural gas and Kohonen maps or classical methods like Voxel Grid. We also reconstructed models acquired by low cost sensors that can be used in virtual and augmented reality environments for redesign or manipulation purposes. Since the NG algorithm has a strong computational cost we propose its acceleration. We have redesigned and implemented the NG learning algorithm to fit it onto Graphics Processing Units using CUDA. A speed-up of 180× faster is obtained compared to the sequential CPU version.

A neural network algorithm to simplify 2D meshes

In this paper we propose a neural network model to simplify and 2D meshes. This model is based on the Growing Neural Gas model and is able to simplify any mesh with different topologies and sizes. A triangulation process is included with the objective to reconstruct the mesh. This model is applied to some problems related to urban networks.

3D Hand Pose Estimation with Neural Networks

We propose the design of a real-time system to recognize and interprethand gestures. The acquisition devices are low cost 3D sensors. 3D hand pose will be segmented, characterized and track using growing neural gas (GNG) structure. The capacity of the system to obtain information with a high degree of freedom allows the encoding of many gestures and a very accurate motion capture. The use of hand pose models combined with motion information provide with GNG permits to deal with the problem of the hand motion representation. A natural interface applied to a virtual mirrorwriting system and to a system to estimate hand pose will be designed to demonstrate the validity of the system.

A three-dimensional representation method for noisy point clouds based on growing self-organizing maps accelerated on GPUs

The research described in this thesis was motivated by the need of a robust model capable of representing 3D data obtained with 3D sensors, which are inherently noisy. In addition, time constraints have to be considered as these sensors are capable of providing a 3D data stream in real time. This thesis proposed the use of Self-Organizing Maps (SOMs) as a 3D representation model. In particular, we proposed the use of the Growing Neural Gas (GNG) network, which has been successfully used for clustering, pattern recognition and topology representation of multi-dimensional data. Until now, Self-Organizing Maps have been primarily computed offline and their application in 3D data has mainly focused on free noise models, without considering time constraints. It is proposed a hardware implementation leveraging the computing power of modern GPUs, which takes advantage of a new paradigm coined as General-Purpose Computing on Graphics Processing Units (GPGPU). The proposed methods were applied to different problem and applications in the area of computer vision such as the recognition and localization of objects, visual surveillance or 3D reconstruction.

Evaluating approximations generated by the GNG3D method for mesh simplification

In this paper we present different error measurements with the aim to evaluate the quality of the approximations generated by the GNG3D method for mesh simplification. The first phase of this method consists on the execution of the GNG3D algorithm, described in the paper. The primary goal of this phase is to obtain a simplified set of vertices representing the best approximation of the original 3D object. In the reconstruction phase we use the information provided by the optimization algorithm to reconstruct the faces thus obtaining the optimized mesh. The implementation of three error functions, named Eavg, Emax, Esur, permitts us to control the error of the simplified model, as it is shown in the examples studied.

Computational cost of GNG3D algorithm for mesh simplification

In this paper we present a study of the computational cost of the GNG3D algorithm for mesh optimization. This algorithm has been implemented taking as a basis a new method which is based on neural networks and consists on two differentiated phases: an optimization phase and a reconstruction phase. The optimization phase is developed applying an optimization algorithm based on the Growing Neural Gas model, which constitutes an unsupervised incremental clustering algorithm. The primary goal of this phase is to obtain a simplified set of vertices representing the best approximation of the original 3D object. In the reconstruction phase we use the information provided by the optimization algorithm to reconstruct the faces thus obtaining the optimized mesh. The computational cost of both phases is calculated, showing some examples.

Representation of 2D objects with a topology preserving network

Comunicación presentada en el 2nd International Workshop on Pattern Recognition in Information Systems, Alicante, April, 2002.

A study of a soft computing based method for 3D scenario reconstruction

Several recent works deal with 3D data in mobile robotic problems, e.g., mapping. Data comes from any kind of sensor (time of flight, Kinect or 3D lasers) that provide a huge amount of unorganized 3D data. In this paper we detail an efficient approach to build complete 3D models using a soft computing method, the Growing Neural Gas (GNG). As neural models deal easily with noise, imprecision, uncertainty or partial data, GNG provides better results than other approaches. The GNG obtained is then applied to a sequence. We present a comprehensive study on GNG parameters to ensure the best result at the lowest time cost. From this GNG structure, we propose to calculate planar patches and thus obtaining a fast method to compute the movement performed by a mobile robot by means of a 3D models registration algorithm. Final results of 3D mapping are also shown.

Using GNG to improve 3D feature extraction—Application to 6DoF egomotion

Several recent works deal with 3D data in mobile robotic problems, e.g. mapping or egomotion. Data comes from any kind of sensor such as stereo vision systems, time of flight cameras or 3D lasers, providing a huge amount of unorganized 3D data. In this paper, we describe an efficient method to build complete 3D models from a Growing Neural Gas (GNG). The GNG is applied to the 3D raw data and it reduces both the subjacent error and the number of points, keeping the topology of the 3D data. The GNG output is then used in a 3D feature extraction method. We have performed a deep study in which we quantitatively show that the use of GNG improves the 3D feature extraction method. We also show that our method can be applied to any kind of 3D data. The 3D features obtained are used as input in an Iterative Closest Point (ICP)-like method to compute the 6DoF movement performed by a mobile robot. A comparison with standard ICP is performed, showing that the use of GNG improves the results. Final results of 3D mapping from the egomotion calculated are also shown.