434 research outputs found
Weak Statistical Constraints for Variational Stereo Imaging of Oceanic Waves
We develop an observational technique for the stereoscopic reconstruction of the wave form of oceanic sea states via a variational stereo method. In the context of active surfaces, the shape and radiance of the wave surface are obtained as minimizers of an energy functional that combines image observations and smoothness priors. To obey the quasi Gaussianity of oceanic waves observed in nature, a given statistical wave law is enforced in the stereo variational framework as a weak constraint. Multigrid methods are then used to solve the partial differential equations derived from the optimality conditions of the augmented energy functional. An application of the developed method to two sets of experimental stereo data is finally presented
Shape Calculus for Shape Energies in Image Processing
Many image processing problems are naturally expressed as energy minimization
or shape optimization problems, in which the free variable is a shape, such as
a curve in 2d or a surface in 3d. Examples are image segmentation, multiview
stereo reconstruction, geometric interpolation from data point clouds. To
obtain the solution of such a problem, one usually resorts to an iterative
approach, a gradient descent algorithm, which updates a candidate shape
gradually deforming it into the optimal shape. Computing the gradient descent
updates requires the knowledge of the first variation of the shape energy, or
rather the first shape derivative. In addition to the first shape derivative,
one can also utilize the second shape derivative and develop a Newton-type
method with faster convergence. Unfortunately, the knowledge of shape
derivatives for shape energies in image processing is patchy. The second shape
derivatives are known for only two of the energies in the image processing
literature and many results for the first shape derivative are limiting, in the
sense that they are either for curves on planes, or developed for a specific
representation of the shape or for a very specific functional form in the shape
energy. In this work, these limitations are overcome and the first and second
shape derivatives are computed for large classes of shape energies that are
representative of the energies found in image processing. Many of the formulas
we obtain are new and some generalize previous existing results. These results
are valid for general surfaces in any number of dimensions. This work is
intended to serve as a cookbook for researchers who deal with shape energies
for various applications in image processing and need to develop algorithms to
compute the shapes minimizing these energies
Variational Stereo Imaging of Oceanic Waves with Statistical Constraints
An image processing observational technique for the stereoscopic reconstruction of the wave form of oceanic sea states is developed. The technique incorporates the enforcement of any given statistical wave law modeling the quasi Gaussianity of oceanic waves observed in nature. The problem is posed in a variational optimization framework, where the desired wave form is obtained as the minimizer of a cost functional that combines image observations, smoothness priors and a weak statistical constraint. The minimizer is obtained combining gradient descent and multigrid methods on the necessary optimality equations of the cost functional. Robust photometric error criteria and a spatial intensity compensation model are also developed to improve the performance of the presented image matching strategy. The weak statistical constraint is thoroughly evaluated in combination with other elements presented to reconstruct and enforce constraints on experimental stereo data, demonstrating the improvement in the estimation of the observed ocean surface
Detail-preserving and Content-aware Variational Multi-view Stereo Reconstruction
Accurate recovery of 3D geometrical surfaces from calibrated 2D multi-view
images is a fundamental yet active research area in computer vision. Despite
the steady progress in multi-view stereo reconstruction, most existing methods
are still limited in recovering fine-scale details and sharp features while
suppressing noises, and may fail in reconstructing regions with few textures.
To address these limitations, this paper presents a Detail-preserving and
Content-aware Variational (DCV) multi-view stereo method, which reconstructs
the 3D surface by alternating between reprojection error minimization and mesh
denoising. In reprojection error minimization, we propose a novel inter-image
similarity measure, which is effective to preserve fine-scale details of the
reconstructed surface and builds a connection between guided image filtering
and image registration. In mesh denoising, we propose a content-aware
-minimization algorithm by adaptively estimating the value and
regularization parameters based on the current input. It is much more promising
in suppressing noise while preserving sharp features than conventional
isotropic mesh smoothing. Experimental results on benchmark datasets
demonstrate that our DCV method is capable of recovering more surface details,
and obtains cleaner and more accurate reconstructions than state-of-the-art
methods. In particular, our method achieves the best results among all
published methods on the Middlebury dino ring and dino sparse ring datasets in
terms of both completeness and accuracy.Comment: 14 pages,16 figures. Submitted to IEEE Transaction on image
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Space-time Reconstruction of Oceanic Sea States via Variational Stereo Methods
We present a remote sensing observational method for the measurement of the spatio-temporal dynamics of ocean waves. Variational techniques are used to recover a coherent space-time reconstruction of oceanic sea states given stereo video imagery. The stereoscopic reconstruction problem is expressed in a variational optimization framework. There, we design an energy functional whose minimizer is the desired temporal sequence of wave heights. The functional combines photometric observations as well as spatial and temporal regularizers. A nested iterative scheme is devised to numerically solve, via 3-D multigrid methods, the system of partial differential equations resulting from the optimality condition of the energy functional. The output of our method is the coherent, simultaneous estimation of the wave surface height and radiance at multiple snapshots. We demonstrate our algorithm on real data collected off-shore. Statistical and spectral analysis are performed. Comparison with respect to an existing sequential method is analyzed
Image compression with anisotropic diffusion
Compression is an important field of digital image processing where well-engineered methods with high performance exist. Partial differential equations (PDEs), however, have not much been explored in this context so far. In our paper we introduce a novel framework for image compression that makes use of the interpolation qualities of edge-enhancing diffusion. Although this anisotropic diffusion equation with a diffusion tensor was originally proposed for image denoising, we show that it outperforms many other PDEs when sparse scattered data must be interpolated. To exploit this property for image compression, we consider an adaptive triangulation method for removing less significant pixels from the image. The remaining points serve as scattered interpolation data for the diffusion process. They can be coded in a compact way that reflects the B-tree structure of the triangulation. We supplement the coding step with a number of amendments such as error threshold adaptation, diffusion-based point selection, and specific quantisation strategies. Our experiments illustrate the usefulness of each of these modifications. They demonstrate that for high compression rates, our PDE-based approach does not only give far better results than the widely-used JPEG standard, but can even come close to the quality of the highly optimised JPEG2000 codec
A Variational Approach to 3D Cylindrical Geometry Reconstruction from Multiple Views
In this paper we present a variational technique for the reconstruction of 3D cylindrical surfaces. Roughly speaking by a cylindrical surface we mean a surface that can be parameterized using the projection on a cylinder in terms of two coordinates, (l, ?), representing the displacement and angle in a cylindrical coordinate system respectively. The starting point for our method is a set of different views of a cylindrical surface, as well as a precomputed disparity map estimation between pair of images. The proposed variational technique is based on an energy minimization where we balance on the one hand the regularity of the cylindrical function given by the distance of the surface points to cylinder axis, and on the other hand, the distance between the projection of the surface points on the images and the expected location following the precomputed disparity map estimation between pair of images. One interesting advantage of this approach is that we regularize the 3D surface by means of a bi-dimensional minimization problem. We show some experimental results for large stereo sequences
Real-time Visual Flow Algorithms for Robotic Applications
Vision offers important sensor cues to modern robotic platforms.
Applications such as control of aerial vehicles, visual servoing,
simultaneous localization and mapping, navigation and more
recently, learning, are examples where visual information is
fundamental to accomplish tasks. However, the use of computer
vision algorithms carries the computational cost of extracting
useful information from the stream of raw pixel data. The most
sophisticated algorithms use complex mathematical formulations
leading typically to computationally expensive, and consequently,
slow implementations. Even with modern computing resources,
high-speed and high-resolution video feed can only be used for
basic image processing operations. For a vision algorithm to be
integrated on a robotic system, the output of the algorithm
should be provided in real time, that is, at least at the same
frequency as the control logic of the robot. With robotic
vehicles becoming more dynamic and ubiquitous, this places higher
requirements to the vision processing pipeline.
This thesis addresses the problem of estimating dense visual flow
information in real time. The contributions of this work are
threefold. First, it introduces a new filtering algorithm for the
estimation of dense optical flow at frame rates as fast as 800 Hz
for 640x480 image resolution. The algorithm follows a
update-prediction architecture to estimate dense optical flow
fields incrementally over time. A fundamental component of the
algorithm is the modeling of the spatio-temporal evolution of the
optical flow field by means of partial differential equations.
Numerical predictors can implement such PDEs to propagate current
estimation of flow forward in time. Experimental validation of
the algorithm is provided using high-speed ground truth image
dataset as well as real-life video data at 300 Hz.
The second contribution is a new type of visual flow named
structure flow. Mathematically, structure flow is the
three-dimensional scene flow scaled by the inverse depth at each
pixel in the image. Intuitively, it is the complete velocity
field associated with image motion, including both optical flow
and scale-change or apparent divergence of the image. Analogously
to optic flow, structure flow provides a robotic vehicle with
perception of the motion of the environment as seen by the
camera. However, structure flow encodes the full 3D image motion
of the scene whereas optic flow only encodes the component on the
image plane. An algorithm to estimate structure flow from image
and depth measurements is proposed based on the same filtering
idea used to estimate optical flow.
The final contribution is the spherepix data structure for
processing spherical images. This data structure is the numerical
back-end used for the real-time implementation of the structure
flow filter. It consists of a set of overlapping patches covering
the surface of the sphere. Each individual patch approximately
holds properties such as orthogonality and equidistance of
points, thus allowing efficient implementations of low-level
classical 2D convolution based image processing routines such as
Gaussian filters and numerical derivatives.
These algorithms are implemented on GPU hardware and can be
integrated to future Robotic Embedded Vision systems to provide
fast visual information to robotic vehicles
Minimizing the Multi-view Stereo Reprojection Error for Triangular Surface Meshes
International audienceThis article proposes a variational multi-view stereo vision method based on meshes for recovering 3D scenes (shape and radiance) from images. Our method is based on generative models and minimizes the reprojection error (difference between the observed images and the images synthesized from the reconstruction). Our contributions are twofold. 1) For the first time, we rigorously compute the gradient of the reprojection error for non smooth surfaces defined by discrete triangular meshes. The gradient correctly takes into account the visibility changes that occur when a surface moves; this forces the contours generated by the reconstructed surface to perfectly match with the apparent contours in the input images. 2) We propose an original modification of the Lambertian model to take into account deviations from the constant brightness assumption without explicitly modelling the reflectance properties of the scene or other photometric phenomena involved by the camera model. Our method is thus able to recover the shape and the diffuse radiance of non Lambertian scenes
Joint 4-D variational stereo reconstruction and camera calibration refinement for oceanic sea state measurements
Validating modern oceanographic theories using models produced through stereo computer vision principles has recently emerged. Space-time (4-D) models of the ocean surface may be generated by stacking a series of 3-D reconstructions independently generated for each time instant or, in a more robust manner, by simultaneously processing several snapshots coherently in a true ?4-D reconstruction.? However, the accuracy of these computer-vision-generated models is subject to the estimations of camera parameters, which may be corrupted under the influence of natural factors such as wind and vibrations. Therefore, removing the unpredictable errors of the camera parameters is necessary for an accurate reconstruction. In this paper, we propose a novel algorithm that can jointly perform a 4-D reconstruction as well as correct the camera parameter errors introduced by external factors. The technique is founded upon variational optimization methods to benefit from their numerous advantages: continuity of the estimated surface in space and time, robustness, and accuracy. The performance of the proposed algorithm is tested using synthetic data produced through computer graphics techniques, based on which the errors of the camera parameters arising from natural factors can be simulated
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