# optical flow constraint equation

## Top PDF optical flow constraint equation: ### Computation of Smooth Optical Flow in a Feedback Connected Analog Network

Since there is one equation for two unknowns at each spatial location, the problem is ill-posed, and there are an infinite number of possible solutions lying on the constraint line for every location ( x;y ) . However, by introducing an additional constraint the prob- lem can be regularized and a unique solution can be found. ### Comparison Between The Optical Flow Computational Techniques

( ) ( ) (2) where ( ) denote the partial derivative of ( ) with respect to time, ( ) ( ( ) ( )) and denotes the usual dot product. The normal component ( ) of motion of spatial contours of constant intensity is given by (2) as where s is the normal speed and n is the normal direction. There are two unknown components of V in the gradient constraint equation, constrained by only one linear equation. Further constraints are therefore necessary to solve for both components of V. ### A Novel VLSI Based Eigen Background Using Background Subtraction for Real Time Image Processing Applications

In a video frame, the field of motion vector per pixel or sub-pixel is called optical flow. There are many a methods for computing optical flow among which few are partial differential equation based methods, gradient consistency based methods and least squared methods. The objective in optic flow calculation is to find the 2D-motion field in an image sequence. As a pixel at location (x,y,t) with intensity I (x,y,t) will have moved by δx,δy and δt between the two frames the following image constraint equation can be given: ### A Comparative Analysis of Optical Flow Algorithms for Velocimetry

Several thresholding algorithm that were considered such as Bradley’s Adaptive Thresholding (Bradley, 2006), Gray Image Thresholding using Triangle Method, and Kittler-Illingworth (Kittler, 1986). Kittler- Illingworth thresholding algorithm was chosen as it manages to preserve the profile of the fluid flow while eliminating noise in the image. The thresholding of Kittler-Illingworth’s come from a mixture of two normal distributions having mean and variances, and their respective proportions. It models the two resulting pixel populations, foreground and background, one from those pixels whose brightness level is smaller than threshold and the other with the higher value than the threshold. The value of threshold chosen is based on a value which minimizes the criterion function of the image, automatically givinga recommended threshold level of a given image. The threshold level for the sample imageusing this method was a grayscale level of 171 and the resultant image is shown in Figure 3. As can be seen, the thresholded image retains most of the profile of the flow while eliminating the background noise. ### DDFlow: Learning Optical Flow with Unlabeled Data Distillation

Data Distillation. Since brightness constancy assumption does not hold for occluded pixels and there is no ground truth flow for occluded pixels, we introduce a data distilla- tion loss to address this problem. As shown in the fourth row and the fifth row, occluded prediction can improve the performance on all datasets, especially for occluded pixels. EPE-OCC decreases from 29.36 to 23.93 (by 18.5 %) on Sintel Clean, from 31.86 to 26.74 (by 16.1 %) on Sintel Fi- nal dataset, from 27.04 to 11.31 (by 58.2 %) on KITTI 2012 and from 42.66 to 24.68 (by 42.1 %) on KITTI 2015. Such a big improvement demonstrates the effectiveness of DDFlow. Our distillation strategy works particularly well near im- age boundary, since our teacher model can distill reliable labels for these pixels. For occluded pixels elsewhere, our method is not as effective, but still produces reasonable re- sults to some extent. This is because we crop at random lo- cation for student model, which covers a large amount of occlusions. Exploring new ideas to cope with occluded pix- els at any location can be a promising research direction in the future. ### Onsager's variational principle in soft matter

(equation (3)). As far as these conditions are satisfied, the time evolution equation can be cast in the variational principle. Using the Stokes equation, it can be proved that equation (3) is valid for any objects moving in Newtonian fluids. Therefore the variational principle holds quite generally. For example, the principle holds for objects with many degrees of freedom (such as polymers or membranes), or for the mixture of such objects (such as concentrated solutions of particles or polymers). ### Index Terms— Face Detection, LBP, Spoofing Attack, Liveness Detection, User Interface, Security I

The spoofing attacks are security threat for the face authentications systems in many modes and the problem of anti-spoofing has been significantly treated in the past few years. Due to varying attack scenarios and environment conditions, there is no absolutely superior face anti-spoofing technique. The combination of liveness features from the image quality-based and motion-based visual cues provides a promising direction to enhance the generalization and stability of a face anti-spoofing classifier. Multi-cues integration-based face anti- spoofing approach combines liveness features from three aspects, the image quality feature, the optical flow based face motion feature, and the optical flow-based scene motion feature. Integration based face anti-spoofing detection system is proposed for face anti-spoofing which is preventing system from face spoofing attacks. Liveness detection and anti-spoofing algorithms has more importance for many biometric modes. Specific hardware device can be used to check presence of a living person in front of the system but this approach can be costly. Combination of multiple modalities could be a safe approach. Most of system uses user’s information to match the input sample against a stored model. The anti-spoofing systems rarely make use of information this matching approach helps to use the available information. Face anti-spoofing features handles the available information of real accesses and spoofing attacks, like texture, quality, motion patterns etc. and this information helps a lot to decide the real and fake access of images. Method applies suitable anti-spoofing method which is inexpensive and convenience to use. ### Implementation of Proficient Technique for Fire Detection and Prevention using Optical Flow Estimation

Computational vision-based flame detection has drawn significant attention in the past decade with camera surveillance systems becoming ubiquitous. Where as many discriminating features, such as colour, shape, texture, etc., have been employed in the literature. This paper proposes a set of motion features based on motion estimators. The key idea consists of exploiting the difference between the turbulent, fast, fire motion, and the structured, rigid motion of other objects. Since classical optical flow methods do not model the characteristics of fire motion (e.g., non-smoothness of motion, non-constancy of intensity), two optical flow methods are specifically designed for the fire detection task: optimal mass transport models fire with dynamic texture, while a data-driven optical flow scheme models saturated flames. Then, characteristic features related to the flow magnitudes and directions are computed from the flow fields to discriminate between fire and non-fire motion. The proposed features are tested on a large video database to demonstrate their practical usefulness. Moreover, a novel evaluation method is proposed by fire simulations that allow for a controlled environment to analyze parameter influences, such as flame saturation, spatial resolution, frame rate, and random noise. ### Internetworking Indonesia Journal

verification of a software component developed during the software lifecycle. Usually testing costs often account to high budget in the software development process. In order to minimize the testing costs, researchers and practitioners automate the testing process rather than carry out manual testing. Test Case Generation is the process of automatically generating a collection of test cases which are applied to a system under test. This paper utilizes branch coverage criteria using the Generalized Optimization Meta heuristic (GOM) algorithm and code constraint graph (CCG) to efficiently maximize the coverage of all the branches. The experimental results show that the proposed test generation technique is effective in generating tests for an application at large. ### A Multi-objective Imperialist Competitive Algorithm for a Capacitated Single-allocation Hub Location Problem

This paper presents a novel multi-objective mathematical model for a capacitated single-allocation hub location problem. There is a vehicle capacity constraint considered in this model. Additionally, our model balances the amount of the incoming flow to the hubs. Moreover, there is a set of available capacities for each potential hub, among which one can be chosen. The multiple objectives are to minimize the total cost of the networks regarding minimizing the maximum travel time between nodes. Due to the NP-hard property of this problem, the model is solved by a multi-objective imperialist competitive algorithm (MOICA). To prove its efficiency, the related results are compared with the results obtained by the well-known multi-objective evolutionary algorithm, namely NSGA-II. The results confirm the efficiency and the effectiveness of our proposed MOICA to provide good solutions, especially for medium and large-sized problems. Finally, we conclude that the proposed MOICA finds quality solutions rather than the solutions obtained by the NSGA-II algorithm. ### Bernoulli equation and flow over a mountain

rounding environment, which is in hydrostatic equilibrium. For a large mountain about 10-km wide (a ~ 10 km), the mountain waves may be considered as hydrostatic nonrotating waves in linear theory (Gill 1982). The con- stant phase lines are tilted upstream with height, thus producing a high pressure on the windward slope and a low pressure on the lee slope. The flow decelerates over the windward slope and accelerates over the lee slope. The ground level pressure perturbation and wind vanish at the peak (Gill 1982; Lin 2007). The linearized equa- tions also show that the decrease of the wind on the windward slope is equal to the increase of wind on the lee side. However, they are different from the nonlinear model simulations, in which the increase of wind on the lee slope is much larger than the decrease on the wind- ward slope; the positive wind perturbation extends to the mountain peak, as shown in Durran (1986), Hsu and Sun (2001), etc. But, it was mostly ignored because the conventional theory states that the change of kinetic en- ergy comes from the decrease of potential energy. The patterns of the surface wind and pressure simulated from nonlinear models with a = 10 km are close to the pattern of the linear, nonhydrostatic waves with a ~ 1 km than the hydrostatic waves discussed in Queney (1948), Gill (1982), etc. The increase of U at the peak further re- duces the pressure according to Bernoulli equation and results in sucking more air from the lower layer in the upstream. Because the pressure p f is lower than the ### Multi Object Detection And Tracking Using Optical Flow Density – Hungarian Kalman Filter (Ofd - Hkf) Algorithm For Vehicle Counting

Intelligent Transportation Systems (ITS) merupakan salah satu topik penelitian yang terus berkembang seiring dengan kemajuan teknologi dan informasi digital. Beberapa manfaat yang diperoleh dari penelitian ITS diantaranya adalah untuk mengatasi beberapa permasalahan terkait dengan keadaan lalu lintas. Pendeteksian dan pelacakan kendaraan merupakan salah satu langkah untuk mewujudkan manfaat dari ITS. Keberadaaan bayangan, perubahan iluminasi, perubahan cuaca, motion blur, dan backgound yang dinamis merupakan tantangan dalam peneteksian dan pelackan objek. Pendeteksian kendaraan pada penelitian ini menggunakan algoritma Optical Flow Density dengan memanfaatkan gradient perpindahan objek pada frame video. Fitur gradient image dan ruangwarna HSV pada algoritma Optical Flow Density menjamin pendeteksian objek pada kondisi perubahan iluminasi dan perubahan cuaca untuk hasil akurasi yang lebih robust. Algoritma Hungarian kalman filter digunakan untuk pelacakan kendaraan. Pelacakan kendaraan digunakan untuk menyelesaikan permasalahan miss detection yang disebabkan karena motion blur dan background yang dinamis. Hungarian kalman filter mengkombinasikan metode state estimation dengan optimal assignment. Prediksi posisi objek di masa depan dapat mendeteksi objek walaupun terjadi miss detection. Perhitungan kendaraan menggunakan Single Line Counting setelah kendaraan berhasil melewati garis tersebut. Rata-rata akurasi untuk masing-masing proses adalah 93,6% untuk pendeteksian, 88,2% untuk pelacakan, dan 88,2% untuk perhitungan kendaraan. ### Integral equation techniques in groundwater flow

Solutions to transient flow problems may be calculated by using Laplace transforms to remove the time dependence from the governing partial differential equation and then using integral [r] ### Design and simulation of low power consumption polymeric based MMI thermo optic switch

Optical switches are crucial components in optical networks. The ability to reconfigure optical switches with low power consumption has become a significant issue and is highly desirable. Furthermore switches with a small footprint are important for space, satellite and flight based applications. Therefore, the employment of Multimode Interference (MMI) thermo-optic switch in integrated optical circuit are required since they offer small size, robustness, good power balance, low polarization sensitivity, low insertion loss and ease of fabrication. In this project, the effect of single heater electrodes in terms of structure and placement will be analyzed to achieve low switching power consumption and crosstalk. ### 4. Analytical similarity solution of non-linear equation using one-parameter infinitesimal Lie group of transformation

The main aim of this paper is to find the analytical similarity solution using the method of infinitesimal transformations of partial differential equations. The partial differential equation is reduced to ordinary equation under this transformation. The resulting ordinary differential equation is an Abel’s equation of second kind whose analytical solution under certain transformation is obtained. ### ME-TE-Thermal engineering

Mathematical description of fluid flow and heat transfer – continuity equation, momentum equation, energy equation, particular laws; Non-dimensional form of equations; Averaged equations for turbulent flows; Solution of a set of linear algebraic equations – (TDMA);Fundamentals of Discretization – Finite Difference Technique: Finite difference methods; different means for formulating finite difference equation; Finite Volume Method - Some Conceptual Basics; Physical consistency, Overall balance, finite volume discretization of a 1-D steady state diffusion problem; Basics of Mesh Generation – Structured grids, body fitted coordinate grids for complex geometries, block structured grids, unstructured grids – discretisation in unstructured grids.Finite volume method for diffusion problems - One- dimensional steady state diffusion with and without sources other than those arising from boundary conditions; handling of boundary conditions; Finite volume method for convection – diffusion problems – Steady one dimensional advection and diffusion – central differencing scheme, upwind differencing scheme – concept of false diffusion, Exponential scheme, Hybrid scheme, the power-law scheme; Higher order schemes – QUICK scheme. ### On the stability and uniqueness of the flow of a fluid through a porous medium

in a porous media is expected to be slow. However, as shown by Munaf, et al. , inertial effects can become important in the flow of fluids through porous media under certain circumstances. In fact, in problems such as enhanced oil recovery where the oil is driven by steam at high pressure, when the pressure gradients are high or when the flow of dense fluids is considered, inertial ef- fects can become important, or at least significant enough to be not ignored. It might be necessary, in flows involving high pressures and high pressure gradients, to include the effect of the pressure on the viscosity as well as the “Drag” term that arises due to frictional effects at the pore. Recently, Subramaniam and Rajagopal  investigated flow of fluids at high pressures while the gradients of pressure is also high and allowed for the viscosity and the “Drag coefficient” to depend on the pressure. They found the results to be markedly different from the results for the constant viscosity and con- stant “Drag coefficient” in that the flow rates are very different and they also found the development of boundary layers (regions where the vorticity is much larger than the rest of the flow domain) wherein the high pressures are confined. Later, Kannan and Rajagopal  also studied the flow of fluids through an inclined porous media at high pressures and pressure gradients due to the effects of gravity and they also found results that show the devel- opment of boundary layers wherein the vorticity is concentrated. The flows considered by Subramaniam and Rajagopal  and Kannan and Rajagopal  are steady flows and due to the special form assumed for the flow field, the inertial term is identically zero. However, the flow field assumed in these and several other studies can only be viewed as approximations to flows that take place in a porous medium as they assume that the flow is unidirectional. It is important to recognize that flows through porous media are inherently unsteady and thus one has to include at the very least the unsteady part of the inertial term. Moreover, flow through porous media is never truly one-dimensional and thus one cannot neglect the non-linear term in the in- ertia on that basis. In fact, when very high pressure gradients are involved the flow will be turbulent. Here, we shall not consider turbulent flows. We shall however modify Brinkman’s equation to take into account the effects of inertia. A detailed discussion of the various assumptions that go into the development of Brinkman’s equation can be found in the recent article on a hierarchy for approximations for the flow of fluids through porous media by Rajagopal  1 . Brinkman very astutely observed that “Equation (2) 2 , ### Learning, Moving, And Predicting With Global Motion Representations

to a target domain by applying a series of elementary differentiable operations (typically additions, multiplications, spatial pooling, and nonlinearities). DNNs are typically trained by comparing this output to a target using a differentiable loss function (such as the cross-entropy loss for classification or the mean-squared error loss for regression) and then minimizing the resulting loss by stochastic gradient descent (SGD) using the backpropagation algorithm (Rumelhart et al. 1986). In so doing, the parameters of the neural network are changed so that full system is able to perform the target task. This results in the development of latent representations in the internal layers of the network. The output of intermediate layers for DNNs trained in this way on image processing tasks can show selectivity for useful intermediate features (Zeiler and Fergus 2014; Zhou et al. 2015; Olah et al. 2018), and the resulting latent representations have proved to be useful for transfer to other tasks and representations (e.g. Long et al. 2015) and as functional explanations of the activity of brain areas (Yamins and DiCarlo 2016). A DNN trained to perform a task that relies on the perception of dynamic content, such as action recognition, can learn to represent features similar to those seen in explicit represntation models without being told about quantities such as optical flow (Karpathy et al. 2014; Varol et al. 2018). ### A master equation for a two-sided optical cavity.

Quantum optical systems, like trapped ions, are routinely described by master equations. The purpose of this paper is to introduce a master equation for two-sided optical cavities with spontaneous photon emission. To do so, we use the same notion of photons as in linear optics scattering theory and consider a continuum of travelling-wave cavity photon modes. Our model predicts the same stationary state photon emission rates for the different sides of a laser-driven optical cavity as classical theories. Moreover, it predicts the same time evolution of the total cavity photon number as the standard standing-wave description in experiments with resonant and near-resonant laser driving. The proposed resonator Hamiltonian can be used, for example, to analyse coherent cavity-fiber networks [E. Kyoseva et al., New J. Phys. 14, 023023 (2012)]. 