Non-uniform Sampling Density Research Articles

Scale-Invariant Features and Polar Descriptors in Omnidirectional Imaging

We propose a method to compute scale-invariant features in omnidirectional images. We present a formulation based on the Riemannian geometry for the definition of differential operators on non-Euclidian manifolds that adapt to the mirror and lens structures in omnidirectional imaging. These operators lead to a scale-space analysis that preserves the geometry of the visual information in omnidirectional images. We then build a novel scale-invariant feature detection framework for omnidirectional images that can be mapped on the sphere. We further present a new descriptor and feature matching solution for these omnidirectional images. The descriptor builds on the log-polar planar descriptors and adapts the descriptor computation to the specific geometry and the nonuniform sampling density of omnidirectional images. We also propose a rotation-invariant matching method that eliminates the orientation computation during the feature detection phase and thus decreases the computational complexity. Experimental results demonstrate that the new feature computation method combined with the adapted descriptors offers promising detection and matching performance, i.e., it improves on the common scale-invariant feature transform (SIFT) features computed on the unwrapped omnidirectional images, as well as spherical SIFT features. Finally, we show that the proposed framework also permits to match features between images with different native geometry.

Efficient sample density estimation by combining gridding and an optimized kernel

The reconstruction of non-Cartesian k-space trajectories often requires the estimation of nonuniform sampling density. Particularly for 3D, this calculation can be computationally expensive. The method proposed in this work combines an iterative algorithm previously proposed by Pipe and Menon (Magn Reson Med 1999;41:179-186) with the optimal kernel design previously proposed by Johnson and Pipe (Magn Reson Med 2009;61:439-447). The proposed method shows substantial time reductions in estimating the densities of center-out trajectories, when compared with that of Johnson. It is demonstrated that, depending on the trajectory, the proposed method can provide reductions in execution time by factors of 12 to 85. The method is also shown to be robust in areas of high trajectory overlap, when compared with two analytical density estimation methods, producing a 10-fold increase in accuracy in one case. Initial conditions allow the proposed method to converge in fewer iterations and are shown to be flexible in terms of the accuracy of information supplied. The proposed method is not only one of the fastest and most accurate algorithms, it is also completely generic, allowing any arbitrary trajectory to be density compensated extemporaneously. The proposed method is also simple and can be implemented on parallel computing platforms in a straightforward manner.

Continuous global optimization in surface reconstruction from an oriented point cloud

We introduce a continuous global optimization method to the field of surface reconstruction from discrete noisy cloud of points with weak information on orientation. The proposed method uses an energy functional combining flux-based data-fit measures and a regularization term. A continuous convex relaxation scheme assures the global minima of the geometric surface functional. The reconstructed surface is implicitly represented by the binary segmentation of vertices of a 3D uniform grid and a triangulated surface can be obtained by extracting an appropriate isosurface. Unlike the discrete graph-cut solution, the continuous global optimization entails advantages like memory requirements, reduction of metrication errors for geometric quantities, and allowing globally optimal surface reconstruction at higher grid resolutions. We demonstrate the performance of the proposed method on several oriented point clouds captured by laser scanners. Experimental results confirm that our approach is robust to noise, large holes and non-uniform sampling density under the condition of very coarse orientation information.

Retinally reconstructed images: digital images having a resolution match with the human eye

Current digital image/video storage, transmission and display technologies use uniformly sampled images. On the other hand, the human retina has a nonuniform sampling density that decreases dramatically as the solid angle from the visual fixation axis increases. Therefore, there is sampling mismatch. This paper introduces retinally reconstructed images (RRI), a representation of digital images that enables a resolution match with the retina. To create an RRI, the size of the input image, the viewing distance and the fixation point should be known. In the coding phase, we compute the codes, which consist of the retinal sampling locations onto which the image projects, together with the retinal outputs at these locations. In the decoding phase, we use the backprojection of the retinal onto the input image grid as B-spline control coefficients, in order to construct a 3D B-spline surface with nonuniform resolution properties. An RRI is then created by mapping the B-spline surface onto a uniform grid, using triangulation. Transmitting or storing the codes instead of the full resolution images enables up to two orders of magnitude data compression, depending on the resolution of the input image, the size of the input image and the viewing distance. The data reduction capability of retinal and RRI is promising for digital video storage and transmission applications. However, the computational burden can be substantial in the decoding phase.

Magnetic resonance fluoroscopy using spirals with variable sampling densities.

The imaging of dynamic processes in the body is of considerable interest in interventional examinations as well as kinematic studies, and spiral imaging is a fast magnetic resonance imaging technique ideally suited for such fluoroscopic applications. In this manuscript, magnetic resonance fluoroscopy pulse sequences in which interleaved spirals are used to continuously acquire data and reconstruct one movie frame for each repetition time interval are implemented. For many applications, not all of k-space needs to be updated each frame, and nonuniform k-space sampling can be used to exploit this rapid imaging strategy by allowing variable update rates for different spatial frequencies. Using the appropriate reconstruction algorithm, the temporal updating rate for each spatial frequency is effectively proportional to the corresponding k-space sampling density. Results from a motion phantom as well as in in vivo gadolinium diethylenetriaminopentaacetic acid (Gd-DTPA) bolus tracking studies in a rat model demonstrate the high temporal resolution achievable using these techniques as well as the tradeoffs available with nonuniform sampling densities. This paper focuses on the acquisition of real-time dynamic information, and all images presented are reconstructed retrospectively. The issues of real-time data reconstruction and display are not addressed.