Search results for: Motion Detection

Authors: Mohammad Saleh Vahdatpour, Yanqing Zhang

Abstract:

Understanding the neural mechanisms underlying motion detection in the human visual system has long been a fascinating challenge in neuroscience and artificial intelligence. This paper presents a spiking neural network model inspired by the processing of motion information in the primate visual system, particularly focusing on the Middle Temporal (MT) area. In our study, we propose a multi-layer spiking neural network model to perform motion detection tasks, leveraging the idea that synaptic delays in neuronal communication are pivotal in motion perception. Synaptic delay, determined by factors like axon length and myelin insulation, affects the temporal order of input spikes, thereby encoding motion direction and speed. Overall, our spiking neural network model demonstrates the feasibility of capturing motion detection principles observed in the primate visual system. The combination of synaptic delays, learning mechanisms, and shared weights and delays in SMD provides a promising framework for motion perception in artificial systems, with potential applications in computer vision and robotics.

Keywords: neural network, motion detection, signature detection, convolutional neural network

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Authors: Koichi Kurita

Abstract:

In this study, we propose a real-time data collection technique for the detection of human walking motion from the charge generated on the human body. This technique is based on the detection of a sub-picoampere electrostatic induction current, generated by the motion, flowing through the electrode of a wireless portable sensor attached to the subject. An FFT analysis of the wave-forms of the electrostatic induction currents generated by the walking motions showed that the currents generated under normal and restricted walking conditions were different. Moreover, we carried out a cepstrum analysis to detect any differences in the walking style. Results suggest that a slight difference in motion, either due to the individual’s gait or a splinted leg, is directly reflected in the electrostatic induction current generated by the walking motion. The proposed wireless portable sensor enables the detection of even subtle differences in walking motion.

Keywords: human walking motion, motion measurement, current measurement, electrostatic induction

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Authors: M. V. Chidananda Murthy, M. Z. Kurian, H. S. Guruprasad

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Image restoration in the process of communication is one of the emerging fields in the image processing. The motion analysis processing is the simplest case to detect motion in an image. Applications of motion analysis widely spread in many areas such as surveillance, remote sensing, film industry, navigation of autonomous vehicles, etc. The scene may contain multiple moving objects, by using motion analysis techniques the blur caused by the movement of the objects can be enhanced by filling-in occluded regions and reconstruction of transparent objects, and it also removes the motion blurring. This paper presents the design and comparison of various motion detection and enhancement filters. Median filter, Linear image deconvolution, Inverse filter, Pseudoinverse filter, Wiener filter, Lucy Richardson filter and Blind deconvolution filters are used to remove the blur. In this work, we have considered different types and different amount of blur for the analysis. Mean Square Error (MSE) and Peak Signal to Noise Ration (PSNR) are used to evaluate the performance of the filters. The designed system has been implemented in Matlab software and tested for synthetic and real-time images.

Keywords: image enhancement, motion analysis, motion detection, motion estimation

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Authors: Jianrong Wu, Xuan Fu, Akihiro Higashi, Zhiming Tan

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CMOS image sensors with a rolling shutter are used broadly in the digital cameras embedded in mobile devices. The rolling shutter suffers the flicker artifacts from the fluorescent lamp, and it could be observed easily. In this paper, the characteristics of illumination flicker in motion case were analyzed, and two efficient detection methods based on matching fragment selection were proposed. According to the experimental results, our methods could achieve as high as 100% accuracy in static scene, and at least 97% in motion scene.

Keywords: illumination flicker, embedded camera, rolling shutter, detection

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Authors: Anton Stadler, Thorsten Ike

Abstract:

In this paper, we present a video based smoke detection algorithm based on TVL1 optical flow estimation. The main part of the algorithm is an accumulating system for motion angles and upward motion speed of the flow field. We optimized the usage of TVL1 flow estimation for the detection of smoke with very low smoke density. Therefore, we use adapted flow parameters and estimate the flow field on difference images. We show in theory and in evaluation that this improves the performance of smoke detection significantly. We evaluate the smoke algorithm using videos with different smoke densities and different backgrounds. We show that smoke detection is very reliable in varying scenarios. Further we verify that our algorithm is very robust towards crowded scenes disturbance videos.

Keywords: low density, optical flow, upward smoke motion, video based smoke detection

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Authors: Jie Yang, Jian-Min Meng

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A GPU-based floating object detection scheme is presented in this paper which is designed for floating mine detection tasks. This system uses contrast and motion information to eliminate as many false positives as possible while avoiding false negatives. The GPU computation platform is deployed to allow detecting objects in real-time. From the experimental results, it is shown that with certain configuration, the GPU-based scheme can speed up the computation up to one thousand times compared to the CPU-based scheme.

Keywords: object detection, GPU, motion estimation, parallel processing

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Authors: Hiroyuki Aoki

Abstract:

The glass transition phenomenon has been extensively studied for a long time. The glass transition of polymer materials is assigned to the transition of the dynamics of the chain backbone segment. However, the detailed mechanism of the transition behavior of the segmental motion is still unclear. In the current work, the single molecule detection technique was employed to reveal the trajectory of the molecular motion of the single polymer chain. The center segment of poly(butyl methacrylate) chain was labeled by a perylenediimide dye molecule and observed by a highly sensitive fluorescence microscope in a defocus condition. The translational and rotational diffusion of the center segment in a single polymer chain was analyzed near the glass transition temperature. The direct observation of the individual polymer chains revealed the intermittent behavior of the segmental motion, indicating the spatial inhomogeneity.

Keywords: glass transition, molecular motion, polymer materials, single molecule

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Authors: Hyojin Lim, Cuong Nguyen Khac, Yeongyu Choi, Ho-Youl Jung

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In this paper, we propose a simple moving object detection, which is based on motion vectors obtained from pyramidal Lucas-Kanade optical flow. The proposed method detects moving objects such as pedestrians, the other vehicles and some obstacles at the front-side of the host vehicle, and it can provide the warning to the driver. Motion vectors are obtained by using pyramidal Lucas-Kanade optical flow, and some outliers are eliminated by comparing the amplitude of each vector with the pre-defined threshold value. The background model is obtained by calculating the mean and the variance of the amplitude of recent motion vectors in the rectangular shaped local region called the cell. The model is applied as the reference to classify motion vectors of moving objects and those of background. Motion vectors are clustered to rectangular regions by using the unsupervised clustering K-means algorithm. Labeling method is applied to label groups which is close to each other, using by distance between each center points of rectangular. Through the simulations tested on four kinds of scenarios such as approaching motorbike, vehicle, and pedestrians to host vehicle, we prove that the proposed is simple but efficient for moving object detection in parking lots.

Keywords: moving object detection, dynamic scene, optical flow, pyramidal optical flow

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Authors: Arwa Alzughaibi

Abstract:

Human Motion detection is a challenging task due to a number of factors including variable appearance, posture and a wide range of illumination conditions and background. So, the first need of such a model is a reliable feature set that can discriminate between a human and a non-human form with a fair amount of confidence even under difficult conditions. By having richer representations, the classification task becomes easier and improved results can be achieved. The Aim of this paper is to investigate the reliable and accurate human motion detection models that are able to detect the human motions accurately under varying illumination levels and backgrounds. Different sets of features are tried and tested including Histogram of Oriented Gradients (HOG), Deformable Parts Model (DPM), Local Decorrelated Channel Feature (LDCF) and Aggregate Channel Feature (ACF). However, we propose an efficient and reliable human motion detection approach by combining Histogram of oriented gradients (HOG) and local phase quantization (LPQ) as the feature set, and implementing search pruning algorithm based on optical flow to reduce the number of false positive. Experimental results show the effectiveness of combining local phase quantization descriptor and the histogram of gradient to perform perfectly well for a large range of illumination conditions and backgrounds than the state-of-the-art human detectors. Areaunder th ROC Curve (AUC) of the proposed method achieved 0.781 for UCF dataset and 0.826 for CDW dataset which indicates that it performs comparably better than HOG, DPM, LDCF and ACF methods.

Keywords: human motion detection, histograms of oriented gradient, local phase quantization, local phase quantization

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Authors: Yuan-Hsiang Chang, Pin-Chi Lin, Li-Der Jeng

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Advance in techniques of image and video processing has enabled the development of intelligent video surveillance systems. This study was aimed to automatically detect moving human objects and to analyze events of dual human interaction in a surveillance scene. Our system was developed in four major steps: image preprocessing, human object detection, human object tracking, and motion trajectory analysis. The adaptive background subtraction and image processing techniques were used to detect and track moving human objects. To solve the occlusion problem during the interaction, the Kalman filter was used to retain a complete trajectory for each human object. Finally, the motion trajectory analysis was developed to distinguish between the interaction and non-interaction events based on derivatives of trajectories related to the speed of the moving objects. Using a database of 60 video sequences, our system could achieve the classification accuracy of 80% in interaction events and 95% in non-interaction events, respectively. In summary, we have explored the idea to investigate a system for the automatic classification of events for interaction and non-interaction events using surveillance cameras. Ultimately, this system could be incorporated in an intelligent surveillance system for the detection and/or classification of abnormal or criminal events (e.g., theft, snatch, fighting, etc.).

Keywords: motion detection, motion tracking, trajectory analysis, video surveillance

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Authors: T. Gangadhararao, K. Krishna Kishore

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Motion Estimation (ME) plays a critical role in a video coder, testing such a module is of priority concern. While focusing on the testing of ME in a video coding system, this work presents an error detection and data recovery (EDDR) design, based on the residue-and-quotient (RQ) code, to embed into ME for video coding testing applications. An error in processing Elements (PEs), i.e. key components of a ME, can be detected and recovered effectively by using the proposed EDDR design. The proposed EDDR design for ME testing can detect errors and recover data with an acceptable area overhead and timing penalty.

Keywords: area overhead, data recovery, error detection, motion estimation, reliability, residue-and-quotient (RQ) code

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Authors: A. Harras, A. Tsuji, K. Terada

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Tracking of moving people has gained a matter of great importance due to rapid technological advancements in the field of computer vision. The objective of this study is to design a motion based detection and tracking multiple walking pedestrians randomly in different directions. In our proposed method, Gaussian mixture model (GMM) is used to determine moving persons in image sequences. It reacts to changes that take place in the scene like different illumination; moving objects start and stop often, etc. Background noise in the scene is eliminated through applying morphological operations and the motions of tracked people which is determined by using the Kalman filter. The Kalman filter is applied to predict the tracked location in each frame and to determine the likelihood of each detection. We used a benchmark data set for the evaluation based on a side wall stationary camera. The actual scenes from the data set are taken on a street including up to eight people in front of the camera in different two scenes, the duration is 53 and 35 seconds, respectively. In the case of walking pedestrians in close proximity, the proposed method has achieved the detection ratio of 87%, and the tracking ratio is 77 % successfully. When they are deferred from each other, the detection ratio is increased to 90% and the tracking ratio is also increased to 79%.

Keywords: automatic detection, tracking, pedestrians, counting

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Authors: Nantakrit Yodpijit, Teppakorn Sittiwanchai

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The number of older adults is rising rapidly. The world’s population becomes aging. Falls is one of common and major health problems in the elderly. Falls may lead to acute and chronic injuries and deaths. The fall-prone individuals are at greater risk for decreased quality of life, lowered productivity and poverty, social problems, and additional health problems. A number of studies on falls prevention using fall detection system have been conducted. Many available technologies for fall detection system are laboratory-based and can incur substantial costs for falls prevention. The utilization of alternative technologies can potentially reduce costs. This paper presents the new design and development of a wearable-based fall detection system using an Accelerometer and Gyroscope as motion sensors for the detection of body orientation and movement. Algorithms are developed to differentiate between Activities of Daily Living (ADL) and falls by comparing Threshold-based values with Artificial Neural Networks (ANN). Results indicate the possibility of using the new threshold-based method with neural network algorithm to reduce the number of false positive (false alarm) and improve the accuracy of fall detection system.

Keywords: aging, algorithm, artificial neural networks (ANN), fall detection system, motion sensorsthreshold

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Authors: Koichi Kurita

Abstract:

In this study, an effective non-contact technique for the detection of human physical activity is proposed. The technique is based on detecting the electrostatic induction current generated by the walking motion under non-contact and non-attached conditions. A theoretical model for the electrostatic induction current generated because of a change in the electric potential of the human body is proposed. By comparing the obtained electrostatic induction current with the theoretical model, it becomes obvious that this model effectively explains the behavior of the waveform of the electrostatic induction current. The normal walking motions are recorded using a portable sensor measurement located in a passageway　of office building. The obtained results show that detailed information regarding physical activity such as a walking cycle can be estimated using our proposed technique. This suggests that the proposed technique which is based on the detection of the walking signal, can be successfully applied to the detection of human walking motion in a secured building.

Keywords: human walking motion, access control, electrostatic induction, alarm monitoring

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Authors: Ismahafezi Ismail, Mohd Shahrizal Sunar

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The motion of a realistic 3D humanoid character is very important especially for the industries developing computer animations and games. However, this type of motion is seen with a very complex dimensional data as well as body position, orientation, and joint rotation. Integrated Style Motion Editor (ISME), on the other hand, is a method used to alter the 3D humanoid motion capture data utilised in computer animation and games development. Therefore, this study was carried out with the purpose of demonstrating a method that is able to manipulate and deform different motion styles by integrating Key Pose Deformation Technique and Trajectory Control Technique. This motion editing method allows the user to generate new motions from the original motion capture data using a simple interface control. Unlike the previous method, our method produces a realistic humanoid motion style in real time.

Keywords: computer animation, humanoid motion, motion capture, motion editing

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Authors: Insaf Bellamine, Hamid Tairi

Abstract:

Detecting moving objects in sequences is an essential step for video analysis. This paper mainly contributes to the Color Space-Time Interest Points (CSTIP) extraction and detection. We propose a new method for detection of moving objects. Two main steps compose the proposed method. First, we suggest to apply the algorithm of the detection of Color Space-Time Interest Points (CSTIP) on both components of the Color Structure-Texture Image Decomposition which is based on a Partial Differential Equation (PDE): a color geometric structure component and a color texture component. A descriptor is associated to each of these points. In a second stage, we address the problem of grouping the points (CSTIP) into clusters. Experiments and comparison to other motion detection methods on challenging sequences show the performance of the proposed method and its utility for video analysis. Experimental results are obtained from very different types of videos, namely sport videos and animation movies.

Keywords: Color Space-Time Interest Points (CSTIP), Color Structure-Texture Image Decomposition, Motion Detection, clustering

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Authors: Seyed Nima Tayarani Bathaie

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In this paper, an image-receiving system was designed and implemented through optimization of object detection algorithms using Haar features. This optimized algorithm served as face and eye detection separately. Then, cascading them led to a clear image of the user. Utilization of this feature brought about higher security by preventing fraud. This attribute results from the fact that services will be given to the user on condition that a clear image of his face has already been captured which would exclude the inappropriate person. In order to expedite processing and eliminating unnecessary ones, the input image was compressed, a motion detection function was included in the program, and detection window size was confined.

Keywords: face detection algorithm, Haar features, security of ATM

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Authors: Amritpal Singh Nafria, Rohit Sharma, Md. Shami Ansari

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Up to now only five different equations of motion can be derived from velocity time graph without needing to know the normal and frictional forces acting at the point of contact. In this paper we obtained all possible requisite conditions to be considering an equation as an equation of motion. After that we classified equations of motion by considering two equations as fundamental kinematical equations of motion and other three as additional kinematical equations of motion. After deriving these five equations of motion, we examine the easiest way of solving a wide variety of useful numerical problems. At the end of the paper, we discussed the importance and educational benefits of classification of equations of motion.

Keywords: velocity-time graph, fundamental equations, additional equations, requisite conditions, importance and educational benefits

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Authors: Carolina Gouveia, José Vieira, Pedro Pinho

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The cardiopulmonary signal monitoring, without the usage of contact electrodes or any type of in-body sensors, has several applications such as sleeping monitoring and continuous monitoring of vital signals in bedridden patients. This system has also applications in the vehicular environment to monitor the driver, in order to avoid any possible accident in case of cardiac failure. Thus, the bio-radar system proposed in this paper, can measure vital signals accurately by using the Doppler effect principle that relates the received signal properties with the distance change between the radar antennas and the person’s chest-wall. Once the bio-radar aim is to monitor subjects in real-time and during long periods of time, it is impossible to guarantee the patient immobilization, hence their random motion will interfere in the acquired signals. In this paper, a mathematical model of the bio-radar is presented, as well as its simulation in MATLAB. The used algorithm for breath rate extraction is explained and a method for DC offsets removal based in a motion detection system is proposed. Furthermore, experimental tests were conducted with a view to prove that the unavoidable random motion can be used to estimate the DC offsets accurately and thus remove them successfully.

Keywords: bio-signals, DC component, Doppler effect, ellipse fitting, radar, SDR

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Authors: Mansouri Nabila, Ben Jemaa Yousra, Motamed Cina, Watelain Eric

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Research and development efforts in intelligent Advanced Driver Assistance Systems (ADAS) seek to save lives and reduce the number of on-road fatalities. For traffic and emergency monitoring, the essential but challenging task is vehicle detection and tracking in reasonably short time. This purpose needs first of all a powerful dynamic car detector model. In fact, this paper presents an optimized HOG process based on shape and motion parameters fusion. Our proposed approach mains to compute HOG by bloc feature from foreground blobs using configurable research window and pathway in order to overcome the shortcoming in term of computing time of HOG descriptor and improve their dynamic application performance. Indeed we prove in this paper that HOG by bloc descriptor combined with motion parameters is a very suitable car detector which reaches in record time a satisfactory recognition rate in dynamic outside area and bypasses several popular works without using sophisticated and expensive architectures such as GPU and FPGA.

Keywords: car-detector, HOG, motion, computing time

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Authors: Jinsiang Shaw, Pik-Hoe Chen

Abstract:

This paper aims to integrate human recognition, motion recognition, and object tracking technologies without requiring a pre-training database model for motion recognition or the unknown object itself. Furthermore, it can simultaneously track multiple users and multiple objects. Unlike other existing human motion recognition methods, our approach employs a rule-based condition method to determine if a user hand is approaching or departing an object. It uses a background subtraction method to separate the human and object from the background, and employs behavior features to effectively interpret human object-grabbing actions. With an object’s histogram characteristics, we are able to isolate and track it using back projection. Hence, a moving object trajectory can be recorded and the object itself can be located. This particular technique can be used in a camera surveillance system in a shopping area to perform real-time intelligent surveillance, thus preventing theft. Experimental results verify the validity of the developed surveillance algorithm with an accuracy of 83% for shoplifting detection.

Keywords: Automatic Tracking, Back Projection, Motion Recognition, Shoplifting

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Authors: Jincan Li, Mingyu Gao, Zhiwei He, Yuxiang Yang, Zhongfei Yu, Yuanyuan Liu

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Building an appropriate motion model is crucial for trajectory planning of robots and determines the operational quality directly. An adaptive acceleration and deceleration motion planning based on trigonometric functions for the end-effector of 6-DOF robots in Cartesian coordinate system is proposed in this paper. This method not only achieves the smooth translation motion and rotation motion by constructing a continuous jerk model, but also automatically adjusts the parameters of trigonometric functions according to the variable inputs and the kinematic constraints. The results of computer simulation show that this method is correct and effective to achieve the adaptive motion planning for linear trajectories.

Keywords: kinematic constraints, motion planning, trigonometric function, 6-DOF robots

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Authors: Baris Can Yalcin

Abstract:

Motion sensors have been commonly used as a valuable component in mechatronic systems, however, many mechatronic designs and applications that need motion sensors cost enormous amount of money, especially high-tech systems. Design of a software for communication protocol between data acquisition card and motion sensor is another issue that has to be solved. This study presents how to design a low cost motion data acquisition setup consisting of MPU 6050 motion sensor (gyro and accelerometer in 3 axes) and Arduino Mega2560 microcontroller. Design parameters are calibration of the sensor, identification and communication between sensor and data acquisition card, interpretation of data collected by the sensor.

Keywords: design, mechatronics, motion sensor, data acquisition

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Authors: Ibrahim Hassan

Abstract:

Motion typography is one of the most important types of visual communication based on display. Through the digital display media, we can control the text properties (size, direction, thickness, color, etc.). The use of motion typography in visual communication made it have several images. We need to adjust the terminology and clarify the different differences between them, so relying on the word motion typography -considered a general term- is not enough to separate the different communicative functions of the moving text. In this paper, we discuss the different effects of motion typography on Arabic writing and how we can achieve harmony between the movement and the letterform, and we will, during our experiments, present a new type of text movement.

Keywords: Arabic typography, motion typography, kinetic typography, fluid typography, temporal typography

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Authors: Alireza Abbasi Moshaii, Farshid Najafi

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In this paper a new model for centre of motion creating is proposed. This new method uses cables. So, it is very useful in robots because it is light and has easy assembling process. In the robots which need to be in touch with some things this method is very good. It will be described in the following. The accuracy of the idea is proved by an experiment. This system could be used in the robots which need a fixed point in the contact with some things and make a circular motion. Such as dancer, physician or repair robots.

Keywords: centre of motion, robotic cables, permanent touching, mechatronics engineering

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Authors: Yeongyu Choi, Ju H. Park, S. M. Lee, Ho-Youl Jung

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In this paper, an improved method for estimating fundamental matrix is proposed. The method is applied effectively to monocular camera based moving object detection. The method consists of corner points detection, moving object’s motion estimation and fundamental matrix calculation. The corner points are obtained by using Harris corner detector, motions of moving objects is calculated from pyramidal Lucas-Kanade optical flow algorithm. Through epipolar geometry analysis using RANSAC, the fundamental matrix is calculated. In this method, we have improved the performances of moving object detection by using two threshold values that determine inlier or outlier. Through the simulations, we compare the performances with varying the two threshold values.

Keywords: corner detection, optical flow, epipolar geometry, RANSAC

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Authors: Areena Bhatti

Abstract:

The geometric arrangement of planet and moon is the result of a self-organizing system. In our solar system, the planets and moons are constantly orbiting around the sun. The aim of this theory is to compare the motion of a solar system with the motion of water droplet when poured into a water body. The basic methodology is to compare both motions to know how they are related to each other. The difference between both systems will be that one is extremely fast, and the other is extremely slow. The role of this theory is that by looking at the fast system we can conclude how slow the system will get to an end. Just like ripples are formed around water droplet that move away from the droplet and water droplet forming those ripples become small in size will tell us how solar system will behave in the same way. So it is concluded that large and small systems can work under the same process but with different motions of time, and motion of the solar system is the slowest form of water droplet motion.

Keywords: motion, water, sun, time

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Authors: Insaf Ajili, Malik Mallem, Jean-Yves Didier

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Motion recognition from videos is actually a very complex task due to the high variability of motions. This paper describes the challenges of human motion recognition, especially motion representation step with relevant features. Our descriptor vector is inspired from Laban Movement Analysis method. We propose discriminative features using the Random Forest algorithm in order to remove redundant features and make learning algorithms operate faster and more effectively. We validate our method on MSRC-12 and UTKinect datasets.

Keywords: discriminative LMA features, features reduction, human motion recognition, random forest

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Authors: Yudhajit Datta, Hamsi Iyer, Jonathan Bandi, Ankit Sethia

Abstract:

Motion Tracking and Stereo Vision are complicated, albeit well-understood problems in computer vision. Existing softwares that combine the two approaches to perform stereo motion tracking typically employ complicated and computationally expensive procedures. The purpose of this study is to create a simple and effective solution capable of combining the two approaches. The study aims to explore a strategy to combine the two techniques of two-dimensional motion tracking using Kalman Filter; and depth detection of object using Stereo Vision. In conventional approaches objects in the scene of interest are observed using a single camera. However for Stereo Motion Tracking; the scene of interest is observed using video feeds from two calibrated cameras. Using two simultaneous measurements from the two cameras a calculation for the depth of the object from the plane containing the cameras is made. The approach attempts to capture the entire three-dimensional spatial information of each object at the scene and represent it through a software estimator object. In discrete intervals, the estimator tracks object motion in the plane parallel to plane containing cameras and updates the perpendicular distance value of the object from the plane containing the cameras as depth. The ability to efficiently track the motion of objects in three-dimensional space using a simplified approach could prove to be an indispensable tool in a variety of surveillance scenarios. The approach may find application from high security surveillance scenes such as premises of bank vaults, prisons or other detention facilities; to low cost applications in supermarkets and car parking lots.

Keywords: kalman filter, stereo vision, motion tracking, matlab, object tracking, camera calibration, computer vision system toolbox

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Authors: Mounir Zili

Abstract:

We will introduce a new extension of the Brownian motion, that could serve to get a good model of many natural phenomena. It is a linear combination of a finite number of sub-fractional Brownian motions; that is why we will call it the mixed sub-fractional Brownian motion. We will present some basic properties of this process. Among others, we will check that our process is non-Markovian and that it has non-stationary increments. We will also give the conditions under which it is a semimartingale. Finally, the main features of its sample paths will be specified.

Keywords: mixed Gaussian processes, Sub-fractional Brownian motion, sample paths

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