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.

Constrained self-organizing feature map to preserve feature extraction topology

In many classification problems, it is necessary to consider the specific location of an n-dimensional space from which features have been calculated. For example, considering the location of features extracted from specific areas of a two-dimensional space, as an image, could improve the understanding of a scene for a video surveillance system. In the same way, the same features extracted from different locations could mean different actions for a 3D HCI system. In this paper, we present a self-organizing feature map able to preserve the topology of locations of an n-dimensional space in which the vector of features have been extracted. The main contribution is to implicitly preserving the topology of the original space because considering the locations of the extracted features and their topology could ease the solution to certain problems. Specifically, the paper proposes the n-dimensional constrained self-organizing map preserving the input topology (nD-SOM-PINT). Features in adjacent areas of the n-dimensional space, used to extract the feature vectors, are explicitly in adjacent areas of the nD-SOM-PINT constraining the neural network structure and learning. As a study case, the neural network has been instantiate to represent and classify features as trajectories extracted from a sequence of images into a high level of semantic understanding. Experiments have been thoroughly carried out using the CAVIAR datasets (Corridor, Frontal and Inria) taken into account the global behaviour of an individual in order to validate the ability to preserve the topology of the two-dimensional space to obtain high-performance classification for trajectory classification in contrast of non-considering the location of features. Moreover, a brief example has been included to focus on validate the nD-SOM-PINT proposal in other domain than the individual trajectory. Results confirm the high accuracy of the nD-SOM-PINT outperforming previous methods aimed to classify the same datasets.

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.

Real time motion estimation using a neural architecture implemented on GPUs

This work describes a neural network based architecture that represents and estimates object motion in videos. This architecture addresses multiple computer vision tasks such as image segmentation, object representation or characterization, motion analysis and tracking. The use of a neural network architecture allows for the simultaneous estimation of global and local motion and the representation of deformable objects. This architecture also avoids the problem of finding corresponding features while tracking moving objects. Due to the parallel nature of neural networks, the architecture has been implemented on GPUs that allows the system to meet a set of requirements such as: time constraints management, robustness, high processing speed and re-configurability. Experiments are presented that demonstrate the validity of our architecture to solve problems of mobile agents tracking and motion analysis.

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 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.

Contributions to 3D Data Registration and Representation

Nowadays, new computers generation provides a high performance that enables to build computationally expensive computer vision applications applied to mobile robotics. Building a map of the environment is a common task of a robot and is an essential part to allow the robots to move through these environments. Traditionally, mobile robots used a combination of several sensors from different technologies. Lasers, sonars and contact sensors have been typically used in any mobile robotic architecture, however color cameras are an important sensor due to we want the robots to use the same information that humans to sense and move through the different environments. Color cameras are cheap and flexible but a lot of work need to be done to give robots enough visual understanding of the scenes. Computer vision algorithms are computational complex problems but nowadays robots have access to different and powerful architectures that can be used for mobile robotics purposes. The advent of low-cost RGB-D sensors like Microsoft Kinect which provide 3D colored point clouds at high frame rates made the computer vision even more relevant in the mobile robotics field. The combination of visual and 3D data allows the systems to use both computer vision and 3D processing and therefore to be aware of more details of the surrounding environment. The research described in this thesis was motivated by the need of scene mapping. Being aware of the surrounding environment is a key feature in many mobile robotics applications from simple robotic navigation to complex surveillance applications. In addition, the acquisition of a 3D model of the scenes is useful in many areas as video games scene modeling where well-known places are reconstructed and added to game systems or advertising where once you get the 3D model of one room the system can add furniture pieces using augmented reality techniques. In this thesis we perform an experimental study of the state-of-the-art registration methods to find which one fits better to our scene mapping purposes. Different methods are tested and analyzed on different scene distributions of visual and geometry appearance. In addition, this thesis proposes two methods for 3d data compression and representation of 3D maps. Our 3D representation proposal is based on the use of Growing Neural Gas (GNG) method. This Self-Organizing Maps (SOMs) has been successfully used for clustering, pattern recognition and topology representation of various kind of 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. 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, specially 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 thesis proposes 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). Our proposed geometrical 3D compression method seeks to reduce the 3D information using plane detection as basic structure to compress the data. This is due to our target environments are man-made and therefore there are a lot of points that belong to a plane surface. Our proposed method is able to get good compression results in those man-made scenarios. The detected and compressed planes can be also used in other applications as surface reconstruction or plane-based registration algorithms. Finally, we have also demonstrated the goodness of the GPU technologies getting a high performance implementation of a CAD/CAM common technique called Virtual Digitizing.

Model, Metamodel and Topology

This reply to Gash’s (Found Sci 2013) commentary on Nescolarde-Selva and Usó-Doménech (Found Sci 2013) answers the three questions raised and at the same time opens up new questions.

Effect of Cyclic Topology on Charge-Transfer Properties of Organic Molecular Semiconductors: The Case of Cycloparaphenylene Molecules

We have studied the role played by cyclic topology on charge-transfer properties of recently synthesized π -conjugated molecules, namely the set of [n]cycloparaphenylene compounds, with n the number of phenylene rings forming the curved nanoring. We estimate the charge-transfer rates for holes and electrons migration within the array of molecules in their crystalline state. The theoretical calculations suggest that increasing the size of the system would help to obtain higher hole and electron charge-transfer rates and that these materials might show an ambipolar behavior in real samples, independently of the different mode of packing followed by the [6]cycloparaphenylene and [12]cycloparaphenylene cases studied.