Agustín Salgado

Temporal constraints in large optical flow estimation

The aim of this work is to propose a model for computing the optical flow in a sequence of images. We introduce a new temporal regularizer that is suitable for large displacements. We propose to decouple the spatial and temporal regularizations to avoid an incongruous formulation. For the spatial regularization we use the Nagel–Enkelmann operator and a newly designed temporal regularization. Our model is based on an energy functional that yields a partial differential equation (PDE). This PDE is embedded into a multipyramidal strategy to recover large displacements. A gradient descent technique is applied at each scale to reach the minimum.The aim of this work is to propose a model for computing the optical flow in a sequence of images. We introduce a new temporal regularizer that is suitable for large displacements. We propose to decouple the spatial and temporal regularizations to avoid an incongruous formulation. For the spatial regularization we use the Nagel-Enkelmann operator and a newly designed temporal regularization. Our model is based on an energy functional that yields a partial differential equation (PDE). This PDE is embedded into a multipyramidal strategy to recover large displacements. A gradient descent technique is applied at each scale to reach the minimum.

Symmetric optical flow

One of the main technique used to recover motion analysis from two images or to register them is variational optical flow, where the pixels of one image are matched to the pixels of the second image by minimizing an energy functional. In the standard formulation of variational optical flow, the estimated motion vector field depends on the reference image and is asymmetric. However, in most application the solution should be independent of the reference image. Only few symmetrical formulations of the optical flow has been proposed in the literature, where the solution is constraint to be symmetric using a combination of the flow in both directions. We propose a new symmetric variational formulation of the optical flow problem, where the flow is naturally symmetric. Results on the Yosemite sequence show an improved accuracy of our symmetric flow with respect to standard optical flow algorithm.

Invertibility and Estimation of Two-Parameter Polynomial and Division Lens Distortion Models

In this paper, we study lens distortion for still images considering two well-known distortion models: the two-parameter polynomial model and the two-parameter division model. We study the invertibility of these models, and we mathematically characterize the conditions for the distortion parameters under which the distortion model defines a one-to-one transformation. This ensures that the inverse transformation is well defined and the distortion-free image can be properly computed, which provides robustness to the distortion models. A new automatic method to correct the radial distortion is proposed, and a comparative analysis for this method is extensively performed using the polynomial and the division models. With the aim of obtaining an accurate estimation of the model, we propose an optimization scheme which iteratively improves the parameters to achieve a better matching between the distorted lines and the edge points. The proposed method estimates two-parameter radial distortion models by detecting...

An Iterative Optimization Algorithm for Lens Distortion Correction Using Two-Parameter Models

We present an algorithm to automatically estimate two-parameter radial polynomial and division distortion models in images. The method first detects the longest distorted lines within the image by applying the Hough transform enriched with a radial distortion parameter. Once we have obtained a valid initial solution, a two-parameter model is embedded into an iterative nonlinear optimization schema to improve the solution. The minimization aims at reducing the distance from the points to the lines, adjusting two distortion parameters as well as the coordinates of the center of distortion. Furthermore, this allows us to detect more points on the distorted lines in the image, so that the Hough transform is iteratively repeated to extract a better set of lines until no improvement is achieved. We present some experiments on real images with significant distortion to show the ability of the proposed approach to automatically correct this type of distortion as well as a comparison between the polynomial and division models.

A new energy-based method for 3D motion estimation of incompressible PIV flows

Motion estimation has many applications in fluid analysis, and a lot of work has been carried out using Particle Image Velocimetry (PIV) to capture and measure the flow motion from sequences of 2D images. Recent technological advances allow capturing 3D PIV sequences of moving particles. In the context of 3D flow motion, the assumption of incompressibility is an important physical property that is satisfied by a large class of problems and experiments. Standard motion estimation techniques in computer vision do not take into account the physical constraints of the flow, which is a very interesting and challenging problem. In this paper, we propose a new variational motion estimation technique which includes the incompressibility of the flow as a constraint to the minimization problem. We analyze, from a theoretical point of view, the influence of this constraint and we design a new numerical algorithm for motion estimation which enforces it. The performance of the proposed technique is evaluated from numerical experiments on synthetic and real data.

Preserving accurate motion contours with reliable parameter selection

The use of decreasing functions, for mitigating the regularization at image contours, is typical in many recent optical flow methods. However, finding the correct parameter for getting the best of this strategy is challenging. Most of the methods use default parameters that are conservative, providing results that are not better than traditional approaches. Configurations that clearly enhance discontinuities may produce instabilities in the computed optical flows. This is due to the fact that the regularization process may get cancelled, yielding an ill-posed problem. In this work, we analyze the problem of instabilities and propose a method for efficiently determining the value of the parameter. We show that this approach allows us to obtain well preserved discontinuities at the same time that it avoids the ill-posed problem. The experiments with synthetic sequences demonstrate that the results are accurate and the selected parameter is close to the optimal value.

Robust Detection and Ordering of Ellipses on a Calibration Pattern

The aim of this work is to accurately estimate from an image the parameters of some ellipses and their relative positions with respect to a given pattern. The process is characterized because it is fully automated and is robust against image noise and occlusions. We have built a calibrator pattern with two planes each containing several ordered circles in known 3D positions. Our method is able to estimate the position of every ellipse and to put them into correspondence with the original calibrator circles.

Regularization Strategies for Discontinuity-Preserving Optical Flow Methods

The aim of this paper is to study several strategies for the preservation of flow discontinuities in variational optical flow methods. We analyze the combination of robust functionals and diffusion tensors in the smoothness assumption. Our study includes the use of tensors based on decreasing functions, which has shown to provide good results. However, it presents several limitations and usually does not perform better than other basic approaches. It typically introduces instabilities in the computed motion fields in the form of independent blobs of vectors with large magnitude. We propose two alternatives to overcome these drawbacks: first, a simple approach that combines the decreasing function with a minimum isotropic smoothing, and second, a method that looks for the best parameter configuration that preserves the important motion contours and avoid instabilities. It relies on the input images and the regularization parameter. It is fully automatic, providing a near-optimal value for many sequences, as shown in the experiments. Both proposals allow to detect the contours of the motion field and produce more stable solutions for a large range of parameters. In the experimental results, we present a detailed study and comparison of the different strategies.The aim of this paper is to study several strategies for the preservation of flow discontinuities in variational optical flow methods. We analyze the combination of robust functionals and diffusion tensors in the smoothness assumption. Our study includes the use of tensors based on decreasing functions, which has shown to provide good results. However, it presents several limitations and usually does not perform better than other basic approaches. It typically introduces instabilities in the computed motion fields in the form of independent blobs of vectors with large magnitude. We propose two alternatives to overcome these drawbacks: first, a simple approach that combines the decreasing function with a minimum isotropic smoothing, and second, a method that looks for the best parameter configuration that preserves the important motion contours and avoid instabilities. It relies on the input images and the regularization parameter. It is fully automatic, providing a near-optimal value for many sequences, as shown in the experiments. Both proposals allow to detect the contours of the motion field and produce more stable solutions for a large range of parameters. In the experimental results, we present a detailed study and comparison of the different strategies.

3D motion estimation using a combination of correlation and variational methods for PIV

Estimation of motion has many applications in fluid analysis. Lots of work has been carried out using Particle Image Velocimetry to design experiments which capture and measure the flow motion using 2D images. Recent technological advances allow capturing 3D PIV image sequences of moving particles. In this context, we propose a 3D motion estimation technique based on the combination of an iterative cross-correlation technique and a variational (energy-based) technique. The performance of the proposed technique is measured and illustrated using numerical simulations.

An Efficient Algorithm for Estimating the Inverse Optical Flow

The aim of this work is to propose a method for computing the inverse optical flow between two frames in a sequence. We assume that the image registration has already been obtained in one direction and we need to estimate the mapping in the opposite direction. The direct and inverse mappings can easily be related through a simple warping formula, which allows us to propose a fast and efficient algorithm. Nevertheless, it is not possible to estimate the inverse function in the whole domain due to the presence of occlusions and disocclusions. Occlusions occur because some objects move to the same position in the next frame. On the other hand, disocclusions are the opposite situation: no correspondences can be established because there is no object moving to those positions. In this case, there is a lack of information and the best we can do is to guess their values from the surrounding values. In the experimental results, we use standard synthetic sequences to study the performance of the proposed method, and show that it yields very accurate solutions.The aim of this work is to propose a method for computing the inverse optical flow between two frames in a sequence. We assume that the image registration has already been obtained in one direction and we need to estimate the mapping in the opposite direction. The direct and inverse mappings can easily be related through a simple warping formula, which allows us to propose a fast and efficient algorithm. Nevertheless, it is not possible to estimate the inverse function in the whole domain due to the presence of occlusions and disocclusions. Occlusions occur because some objects move to the same position in the next frame. On the other hand, disocclusions are the opposite situation: no correspondences can be established because there is no object moving to those positions. In this case, there is a lack of information and the best we can do is to guess their values from the surrounding values. In the experimental results, we use standard synthetic sequences to study the performance of the proposed method, and show that it yields very accurate solutions.