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Luo X, Qu H, Wang Y, Yi Z, Zhang J, Zhang M. Supervised Learning in Multilayer Spiking Neural Networks With Spike Temporal Error Backpropagation. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2023; 34:10141-10153. [PMID: 35436200 DOI: 10.1109/tnnls.2022.3164930] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
The brain-inspired spiking neural networks (SNNs) hold the advantages of lower power consumption and powerful computing capability. However, the lack of effective learning algorithms has obstructed the theoretical advance and applications of SNNs. The majority of the existing learning algorithms for SNNs are based on the synaptic weight adjustment. However, neuroscience findings confirm that synaptic delays can also be modulated to play an important role in the learning process. Here, we propose a gradient descent-based learning algorithm for synaptic delays to enhance the sequential learning performance of single spiking neuron. Moreover, we extend the proposed method to multilayer SNNs with spike temporal-based error backpropagation. In the proposed multilayer learning algorithm, information is encoded in the relative timing of individual neuronal spikes, and learning is performed based on the exact derivatives of the postsynaptic spike times with respect to presynaptic spike times. Experimental results on both synthetic and realistic datasets show significant improvements in learning efficiency and accuracy over the existing spike temporal-based learning algorithms. We also evaluate the proposed learning method in an SNN-based multimodal computational model for audiovisual pattern recognition, and it achieves better performance compared with its counterparts.
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Tayarani-Najaran MH, Schmuker M. Event-Based Sensing and Signal Processing in the Visual, Auditory, and Olfactory Domain: A Review. Front Neural Circuits 2021; 15:610446. [PMID: 34135736 PMCID: PMC8203204 DOI: 10.3389/fncir.2021.610446] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2020] [Accepted: 04/27/2021] [Indexed: 11/13/2022] Open
Abstract
The nervous systems converts the physical quantities sensed by its primary receptors into trains of events that are then processed in the brain. The unmatched efficiency in information processing has long inspired engineers to seek brain-like approaches to sensing and signal processing. The key principle pursued in neuromorphic sensing is to shed the traditional approach of periodic sampling in favor of an event-driven scheme that mimicks sampling as it occurs in the nervous system, where events are preferably emitted upon the change of the sensed stimulus. In this paper we highlight the advantages and challenges of event-based sensing and signal processing in the visual, auditory and olfactory domains. We also provide a survey of the literature covering neuromorphic sensing and signal processing in all three modalities. Our aim is to facilitate research in event-based sensing and signal processing by providing a comprehensive overview of the research performed previously as well as highlighting conceptual advantages, current progress and future challenges in the field.
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Affiliation(s)
| | - Michael Schmuker
- School of Physics, Engineering and Computer Science, University of Hertfordshire, Hatfield, United Kingdom
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Liu Q, Pan G, Ruan H, Xing D, Xu Q, Tang H. Unsupervised AER Object Recognition Based on Multiscale Spatio-Temporal Features and Spiking Neurons. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2020; 31:5300-5311. [PMID: 32054587 DOI: 10.1109/tnnls.2020.2966058] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
This article proposes an unsupervised address event representation (AER) object recognition approach. The proposed approach consists of a novel multiscale spatio-temporal feature (MuST) representation of input AER events and a spiking neural network (SNN) using spike-timing-dependent plasticity (STDP) for object recognition with MuST. MuST extracts the features contained in both the spatial and temporal information of AER event flow, and forms an informative and compact feature spike representation. We show not only how MuST exploits spikes to convey information more effectively, but also how it benefits the recognition using SNN. The recognition process is performed in an unsupervised manner, which does not need to specify the desired status of every single neuron of SNN, and thus can be flexibly applied in real-world recognition tasks. The experiments are performed on five AER datasets including a new one named GESTURE-DVS. Extensive experimental results show the effectiveness and advantages of the proposed approach.
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Ramesh B, Yang H, Orchard G, Le Thi NA, Zhang S, Xiang C. DART: Distribution Aware Retinal Transform for Event-Based Cameras. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2020; 42:2767-2780. [PMID: 31144625 DOI: 10.1109/tpami.2019.2919301] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We introduce a generic visual descriptor, termed as distribution aware retinal transform (DART), that encodes the structural context using log-polar grids for event cameras. The DART descriptor is applied to four different problems, namely object classification, tracking, detection and feature matching: (1) The DART features are directly employed as local descriptors in a bag-of-words classification framework and testing is carried out on four standard event-based object datasets (N-MNIST, MNIST-DVS, CIFAR10-DVS, NCaltech-101); (2) Extending the classification system, tracking is demonstrated using two key novelties: (i) Statistical bootstrapping is leveraged with online learning for overcoming the low-sample problem during the one-shot learning of the tracker, (ii) Cyclical shifts are induced in the log-polar domain of the DART descriptor to achieve robustness to object scale and rotation variations; (3) To solve the long-term object tracking problem, an object detector is designed using the principle of cluster majority voting. The detection scheme is then combined with the tracker to result in a high intersection-over-union score with augmented ground truth annotations on the publicly available event camera dataset; (4) Finally, the event context encoded by DART greatly simplifies the feature correspondence problem, especially for spatio-temporal slices far apart in time, which has not been explicitly tackled in the event-based vision domain.
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Bi Y, Chadha A, Abbas A, Bourtsoulatze E, Andreopoulos Y. Graph-based Spatio-Temporal Feature Learning for Neuromorphic Vision Sensing. IEEE TRANSACTIONS ON IMAGE PROCESSING : A PUBLICATION OF THE IEEE SIGNAL PROCESSING SOCIETY 2020; PP:9084-9098. [PMID: 32941136 DOI: 10.1109/tip.2020.3023597] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Neuromorphic vision sensing (NVS) devices represent visual information as sequences of asynchronous discrete events (a.k.a., "spikes") in response to changes in scene reflectance. Unlike conventional active pixel sensing (APS), NVS allows for significantly higher event sampling rates at substantially increased energy efficiency and robustness to illumination changes. However, feature representation for NVS is far behind its APS-based counterparts, resulting in lower performance in high-level computer vision tasks. To fully utilize its sparse and asynchronous nature, we propose a compact graph representation for NVS, which allows for end-to-end learning with graph convolution neural networks. We couple this with a novel end-to-end feature learning framework that accommodates both appearancebased and motion-based tasks. The core of our framework comprises a spatial feature learning module, which utilizes residual-graph convolutional neural networks (RG-CNN), for end-to-end learning of appearance-based features directly from graphs. We extend this with our proposed Graph2Grid block and temporal feature learning module for efficiently modelling temporal dependencies over multiple graphs and a long temporal extent. We show how our framework can be configured for object classification, action recognition and action similarity labeling. Importantly, our approach preserves the spatial and temporal coherence of spike events, while requiring less computation and memory. The experimental validation shows that our proposed framework outperforms all recent methods on standard datasets. Finally, to address the absence of large real-world NVS datasets for complex recognition tasks, we introduce, evaluate and make available the American Sign Language letters (ASL-DVS), as well as human action dataset (UCF101-DVS, HMDB51-DVS and ASLAN-DVS).
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Xiao R, Tang H, Ma Y, Yan R, Orchard G. An Event-Driven Categorization Model for AER Image Sensors Using Multispike Encoding and Learning. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2020; 31:3649-3657. [PMID: 31714243 DOI: 10.1109/tnnls.2019.2945630] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
In this article, we present a systematic computational model to explore brain-based computation for object recognition. The model extracts temporal features embedded in address-event representation (AER) data and discriminates different objects by using spiking neural networks (SNNs). We use multispike encoding to extract temporal features contained in the AER data. These temporal patterns are then learned through the tempotron learning rule. The presented model is consistently implemented in a temporal learning framework, where the precise timing of spikes is considered in the feature-encoding and learning process. A noise-reduction method is also proposed by calculating the correlation of an event with the surrounding spatial neighborhood based on the recently proposed time-surface technique. The model evaluated on wide spectrum data sets (MNIST, N-MNIST, MNIST-DVS, AER Posture, and Poker Card) demonstrates its superior recognition performance, especially for the events with noise.
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A High-Speed Low-Cost VLSI System Capable of On-Chip Online Learning for Dynamic Vision Sensor Data Classification. SENSORS 2020; 20:s20174715. [PMID: 32825560 PMCID: PMC7506740 DOI: 10.3390/s20174715] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/04/2020] [Revised: 08/09/2020] [Accepted: 08/16/2020] [Indexed: 11/21/2022]
Abstract
This paper proposes a high-speed low-cost VLSI system capable of on-chip online learning for classifying address-event representation (AER) streams from dynamic vision sensor (DVS) retina chips. The proposed system executes a lightweight statistic algorithm based on simple binary features extracted from AER streams and a Random Ferns classifier to classify these features. The proposed system’s characteristics of multi-level pipelines and parallel processing circuits achieves a high throughput up to 1 spike event per clock cycle for AER data processing. Thanks to the nature of the lightweight algorithm, our hardware system is realized in a low-cost memory-centric paradigm. In addition, the system is capable of on-chip online learning to flexibly adapt to different in-situ application scenarios. The extra overheads for on-chip learning in terms of time and resource consumption are quite low, as the training procedure of the Random Ferns is quite simple, requiring few auxiliary learning circuits. An FPGA prototype of the proposed VLSI system was implemented with 9.5~96.7% memory consumption and <11% computational and logic resources on a Xilinx Zynq-7045 chip platform. It was running at a clock frequency of 100 MHz and achieved a peak processing throughput up to 100 Meps (Mega events per second), with an estimated power consumption of 690 mW leading to a high energy efficiency of 145 Meps/W or 145 event/μJ. We tested the prototype system on MNIST-DVS, Poker-DVS, and Posture-DVS datasets, and obtained classification accuracies of 77.9%, 99.4% and 99.3%, respectively. Compared to prior works, our VLSI system achieves higher processing speeds, higher computing efficiency, comparable accuracy, and lower resource costs.
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Sun Y, Xue B, Zhang M, Yen GG. A Particle Swarm Optimization-Based Flexible Convolutional Autoencoder for Image Classification. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2019; 30:2295-2309. [PMID: 30530340 DOI: 10.1109/tnnls.2018.2881143] [Citation(s) in RCA: 33] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Convolutional autoencoders (CAEs) have shown their remarkable performance in stacking to deep convolutional neural networks (CNNs) for classifying image data during the past several years. However, they are unable to construct the state-of-the-art CNNs due to their intrinsic architectures. In this regard, we propose a flexible CAE (FCAE) by eliminating the constraints on the numbers of convolutional layers and pooling layers from the traditional CAE. We also design an architecture discovery method by exploiting particle swarm optimization, which is capable of automatically searching for the optimal architectures of the proposed FCAE with much less computational resource and without any manual intervention. We test the proposed approach on four extensively used image classification data sets. Experimental results show that our proposed approach in this paper significantly outperforms the peer competitors including the state-of-the-art algorithms.
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Fast and efficient algorithm for matrix completion via closed-form 2/3-thresholding operator. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2018.10.065] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Afshar S, Hamilton TJ, Tapson J, van Schaik A, Cohen G. Investigation of Event-Based Surfaces for High-Speed Detection, Unsupervised Feature Extraction, and Object Recognition. Front Neurosci 2019; 12:1047. [PMID: 30705618 PMCID: PMC6344467 DOI: 10.3389/fnins.2018.01047] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2018] [Accepted: 12/24/2018] [Indexed: 12/31/2022] Open
Abstract
In this work, we investigate event-based feature extraction through a rigorous framework of testing. We test a hardware efficient variant of Spike Timing Dependent Plasticity (STDP) on a range of spatio-temporal kernels with different surface decaying methods, decay functions, receptive field sizes, feature numbers, and back end classifiers. This detailed investigation can provide helpful insights and rules of thumb for performance vs. complexity trade-offs in more generalized networks, especially in the context of hardware implementation, where design choices can incur significant resource costs. The investigation is performed using a new dataset consisting of model airplanes being dropped free-hand close to the sensor. The target objects exhibit a wide range of relative orientations and velocities. This range of target velocities, analyzed in multiple configurations, allows a rigorous comparison of time-based decaying surfaces (time surfaces) vs. event index-based decaying surface (index surfaces), which are used to perform unsupervised feature extraction, followed by target detection and recognition. We examine each processing stage by comparison to the use of raw events, as well as a range of alternative layer structures, and the use of random features. By comparing results from a linear classifier and an ELM classifier, we evaluate how each element of the system affects accuracy. To generate time and index surfaces, the most commonly used kernels, namely event binning kernels, linearly, and exponentially decaying kernels, are investigated. Index surfaces were found to outperform time surfaces in recognition when invariance to target velocity was made a requirement. In the investigation of network structure, larger networks of neurons with large receptive field sizes were found to perform best. We find that a small number of event-based feature extractors can project the complex spatio-temporal event patterns of the dataset to an almost linearly separable representation in feature space, with best performing linear classifier achieving 98.75% recognition accuracy, using only 25 feature extracting neurons.
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Affiliation(s)
- Saeed Afshar
- Biomedical Engineering and Neuroscience Program, The MARCS Institute for Brain, Behaviour, and Development, Western Sydney University, Sydney, NSW, Australia
| | - Tara Julia Hamilton
- Biomedical Engineering and Neuroscience Program, The MARCS Institute for Brain, Behaviour, and Development, Western Sydney University, Sydney, NSW, Australia
| | - Jonathan Tapson
- Biomedical Engineering and Neuroscience Program, The MARCS Institute for Brain, Behaviour, and Development, Western Sydney University, Sydney, NSW, Australia
| | - André van Schaik
- Biomedical Engineering and Neuroscience Program, The MARCS Institute for Brain, Behaviour, and Development, Western Sydney University, Sydney, NSW, Australia
| | - Gregory Cohen
- Biomedical Engineering and Neuroscience Program, The MARCS Institute for Brain, Behaviour, and Development, Western Sydney University, Sydney, NSW, Australia
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Camunas-Mesa LA, Serrano-Gotarredona T, Ieng SH, Benosman R, Linares-Barranco B. Event-Driven Stereo Visual Tracking Algorithm to Solve Object Occlusion. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2018; 29:4223-4237. [PMID: 29989974 DOI: 10.1109/tnnls.2017.2759326] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Object tracking is a major problem for many computer vision applications, but it continues to be computationally expensive. The use of bio-inspired neuromorphic event-driven dynamic vision sensors (DVSs) has heralded new methods for vision processing, exploiting reduced amount of data and very precise timing resolutions. Previous studies have shown these neural spiking sensors to be well suited to implementing single-sensor object tracking systems, although they experience difficulties when solving ambiguities caused by object occlusion. DVSs have also performed well in 3-D reconstruction in which event matching techniques are applied in stereo setups. In this paper, we propose a new event-driven stereo object tracking algorithm that simultaneously integrates 3-D reconstruction and cluster tracking, introducing feedback information in both tasks to improve their respective performances. This algorithm, inspired by human vision, identifies objects and learns their position and size in order to solve ambiguities. This strategy has been validated in four different experiments where the 3-D positions of two objects were tracked in a stereo setup even when occlusion occurred. The objects studied in the experiments were: 1) two swinging pens, the distance between which during movement was measured with an error of less than 0.5%; 2) a pen and a box, to confirm the correctness of the results obtained with a more complex object; 3) two straws attached to a fan and rotating at 6 revolutions per second, to demonstrate the high-speed capabilities of this approach; and 4) two people walking in a real-world environment.
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Linares-Barranco A, Liu H, Rios-Navarro A, Gomez-Rodriguez F, Moeys DP, Delbruck T. Approaching Retinal Ganglion Cell Modeling and FPGA Implementation for Robotics. ENTROPY 2018; 20:e20060475. [PMID: 33265565 PMCID: PMC7512993 DOI: 10.3390/e20060475] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/21/2018] [Revised: 06/01/2018] [Accepted: 06/15/2018] [Indexed: 11/25/2022]
Abstract
Taking inspiration from biology to solve engineering problems using the organizing principles of biological neural computation is the aim of the field of neuromorphic engineering. This field has demonstrated success in sensor based applications (vision and audition) as well as in cognition and actuators. This paper is focused on mimicking the approaching detection functionality of the retina that is computed by one type of Retinal Ganglion Cell (RGC) and its application to robotics. These RGCs transmit action potentials when an expanding object is detected. In this work we compare the software and hardware logic FPGA implementations of this approaching function and the hardware latency when applied to robots, as an attention/reaction mechanism. The visual input for these cells comes from an asynchronous event-driven Dynamic Vision Sensor, which leads to an end-to-end event based processing system. The software model has been developed in Java, and computed with an average processing time per event of 370 ns on a NUC embedded computer. The output firing rate for an approaching object depends on the cell parameters that represent the needed number of input events to reach the firing threshold. For the hardware implementation, on a Spartan 6 FPGA, the processing time is reduced to 160 ns/event with the clock running at 50 MHz. The entropy has been calculated to demonstrate that the system is not totally deterministic in response to approaching objects because of several bioinspired characteristics. It has been measured that a Summit XL mobile robot can react to an approaching object in 90 ms, which can be used as an attentional mechanism. This is faster than similar event-based approaches in robotics and equivalent to human reaction latencies to visual stimulus.
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Affiliation(s)
| | - Hongjie Liu
- Institute of Neuroinformatics, ETHZ-UZH, CH8057 Zurich, Switzerland
| | - Antonio Rios-Navarro
- Robotic and Technology of Computers Lab, University of Seville, ES41012 Sevilla, Spain
| | | | | | - Tobi Delbruck
- Institute of Neuroinformatics, ETHZ-UZH, CH8057 Zurich, Switzerland
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Shi C, Li J, Wang Y, Luo G. Exploiting Lightweight Statistical Learning for Event-Based Vision Processing. IEEE ACCESS : PRACTICAL INNOVATIONS, OPEN SOLUTIONS 2018; 6:19396-19406. [PMID: 29750138 PMCID: PMC5937990 DOI: 10.1109/access.2018.2823260] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
This paper presents a lightweight statistical learning framework potentially suitable for low-cost event-based vision systems, where visual information is captured by a dynamic vision sensor (DVS) and represented as an asynchronous stream of pixel addresses (events) indicating a relative intensity change on those locations. A simple random ferns classifier based on randomly selected patch-based binary features is employed to categorize pixel event flows. Our experimental results demonstrate that compared to existing event-based processing algorithms, such as spiking convolutional neural networks (SCNNs) and the state-of-the-art bag-of-events (BoE)-based statistical algorithms, our framework excels in high processing speed (2× faster than the BoE statistical methods and >100× faster than previous SCNNs in training speed) with extremely simple online learning process, and achieves state-of-the-art classification accuracy on four popular address-event representation data sets: MNIST-DVS, Poker-DVS, Posture-DVS, and CIFAR10-DVS. Hardware estimation shows that our algorithm will be preferable for low-cost embedded system implementations.
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Affiliation(s)
- Cong Shi
- Schepens Eye Research Institute, Massachusetts Eye and Ear, Department of Ophthalmology, Harvard Medical School, Boston, MA 02114 USA
| | - Jiajun Li
- State Key Laboratory of Computer Architecture, Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100864, China
| | - Ying Wang
- State Key Laboratory of Computer Architecture, Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100864, China
| | - Gang Luo
- Schepens Eye Research Institute, Massachusetts Eye and Ear, Department of Ophthalmology, Harvard Medical School, Boston, MA 02114 USA
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Li H, Liu H, Ji X, Li G, Shi L. CIFAR10-DVS: An Event-Stream Dataset for Object Classification. Front Neurosci 2017; 11:309. [PMID: 28611582 PMCID: PMC5447775 DOI: 10.3389/fnins.2017.00309] [Citation(s) in RCA: 63] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2016] [Accepted: 05/16/2017] [Indexed: 11/13/2022] Open
Abstract
Neuromorphic vision research requires high-quality and appropriately challenging event-stream datasets to support continuous improvement of algorithms and methods. However, creating event-stream datasets is a time-consuming task, which needs to be recorded using the neuromorphic cameras. Currently, there are limited event-stream datasets available. In this work, by utilizing the popular computer vision dataset CIFAR-10, we converted 10,000 frame-based images into 10,000 event streams using a dynamic vision sensor (DVS), providing an event-stream dataset of intermediate difficulty in 10 different classes, named as "CIFAR10-DVS." The conversion of event-stream dataset was implemented by a repeated closed-loop smooth (RCLS) movement of frame-based images. Unlike the conversion of frame-based images by moving the camera, the image movement is more realistic in respect of its practical applications. The repeated closed-loop image movement generates rich local intensity changes in continuous time which are quantized by each pixel of the DVS camera to generate events. Furthermore, a performance benchmark in event-driven object classification is provided based on state-of-the-art classification algorithms. This work provides a large event-stream dataset and an initial benchmark for comparison, which may boost algorithm developments in even-driven pattern recognition and object classification.
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Affiliation(s)
- Hongmin Li
- Department of Precision Instrument, Center for Brain-Inspired Computing Research, Tsinghua UniversityBeijing, China
| | - Hanchao Liu
- Department of Precision Instrument, Center for Brain-Inspired Computing Research, Tsinghua UniversityBeijing, China
| | - Xiangyang Ji
- Department of Precision Instrument, Center for Brain-Inspired Computing Research, Tsinghua UniversityBeijing, China.,Department of Automation, Tsinghua UniversityBeijing, China
| | - Guoqi Li
- Department of Precision Instrument, Center for Brain-Inspired Computing Research, Tsinghua UniversityBeijing, China
| | - Luping Shi
- Department of Precision Instrument, Center for Brain-Inspired Computing Research, Tsinghua UniversityBeijing, China
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