Reprojection Methods Research Articles

Trajectory representation and landmark projection for continuous-time structure from motion

This paper revisits the problem of continuous-time structure from motion, and introduces a number of extensions that improve convergence and efficiency. The formulation with a -continuous spline for the trajectory naturally incorporates inertial measurements, as derivatives of the sought trajectory. We analyze the behavior of split spline interpolation on and on , and a joint spline on , and show that the latter implicitly couples the direction of translation and rotation. Such an assumption can make good sense for a camera mounted on a robot arm, but not for hand-held or body-mounted cameras. Our experiments in the Spline Fusion framework show that a split spline on is preferable over an spline in all tested cases. Finally, we investigate the problem of landmark reprojection on rolling shutter cameras, and show that the tested reprojection methods give similar quality, whereas their computational load varies by a factor of two.

Frameless Volume Visualization.

We have developed a novel visualization system based on the reconstruction of high resolution and high frame rate images from a multi-tiered stream of samples that are rendered framelessly. This decoupling of the rendering system from the display system is particularly suitable when dealing with very high resolution displays or expensive rendering algorithms, where the latency of generating complete frames may be prohibitively high for interactive applications. In contrast to the traditional frameless rendering technique, we generate the lowest latency samples on the optimal sampling lattice in the 3D domain. This approach avoids many of the artifacts associated with existing sample caching and reprojection methods during interaction that may not be acceptable in many visualization applications. Advanced visualization effects are generated remotely and streamed into the reconstruction system using tiered samples with varying latencies and quality levels. We demonstrate the use of our visualization system for the exploration of volumetric data at stable guaranteed frame rates on high resolution displays, including a 470 megapixel tiled display as part of the Reality Deck immersive visualization facility.

Indirect Inference Estimation of Mixed Frequency Stochastic Volatility State Space Models Using MIDAS Regressions and ARCH Models

We examine the relationship between MIDAS regressions and the estimation of state space models applied to mixed frequency data. While in some cases the binding function is known, in general it is not, and therefore indirect inference is called for. The approach is appealing when we consider state space models which feature stochastic volatility, or other non-Gaussian and nonlinear settings where maximum likelihood methods require computationally demanding approximate filters. The stochastic volatility feature is particularly relevant when considering high frequency financial series. In addition, we propose a filtering scheme which relies on a combination of re-projection methods and now-casting MIDAS regressions with ARCH models. We assess the efficiency of our indirect inference estimator for the stochastic volatility model by comparing it with the Maximum Likelihood (ML) estimator in Monte Carlo simulation experiments. The ML estimate is computed with a simulation-based Expectation-Maximization (EM) algorithm, in which the smoothing distribution required in the E step is obtained via a particle forward-filtering/backward-smoothing algorithm. Our Monte Carlo simulations show that the Indirect Inference procedure is very appealing, as its statistical accuracy is close to that of MLE but the former procedure has clear advantages in terms of computational efficiency. An application to forecasting quarterly GDP growth in the Euro area with monthly macroeconomic indicators illustrates the usefulness of our procedure in empirical analysis.

On Reconstruction from Non-uniform Spectral Data

This paper addresses the reconstruction of compactly supported functions from non-uniform samples of their Fourier transform. We briefly investigate the consequences of acquiring non-uniform spectral data. We summarize two often applied reconstruction methods, convolutional gridding and uniform re-sampling, and investigate the reconstruction accuracy as it relates to sampling density. Finally, we provide preliminary results from employing spectral re-projection methods in the reconstruction.

A new reprojection method based on a comparison of popular reprojection models

Reprojection is of interest in several applications such as iterative tomographic reconstruction, dose-calculation in radiotherapy and 3D-display volume-rendering. All numerical implementations of reprojection result in varying degrees of errors. Popular reprojection methods were compared using 128×128 2D-noiseless-numerical uniform-disk and Shepp–Logan phantoms to evaluate errors in external-border, interior and overall regions of the reprojected sinogram, in order to investigate a new method for increasing their accuracy on all regions. Root mean squared errors (RMSE) (with calculated projection as reference) were used. No method gives the least errors in all regions. Smoothing projectors decrease noise but introduce important errors in the border region, whereas other projectors increase errors inside the reprojected sinogram. The overall-error is a trade-off between interior and border errors. The conventional ray-driven (R1) and the bilinear-interpolated pixel driven with 5×5 sub-pixels (L5) provide the highest accuracy for border and interior regions, respectively. These results motivate the implementation of a new reprojection method that uses R1 to project pixels near borders in the sinogram and L5 for the others. Feature borders were localized using the spatial derivatives of sinogram count profile. This method provides the least errors for all regions. The performance of the new method was investigated on iterative reconstruction tasks with MLEM. Results show that the new method can promise more accuracy in terms of RMSE and aliasing reduction of the reconstructed images.

Amortized supersampling

We present a real-time rendering scheme that reuses shading samples from earlier time frames to achieve practical antialiasing of procedural shaders. Using a reprojection strategy, we maintain several sets of shading estimates at subpixel precision, and incrementally update these such that for most pixels only one new shaded sample is evaluated per frame. The key difficulty is to prevent accumulated blurring during successive reprojections. We present a theoretical analysis of the blur introduced by reprojection methods. Based on this analysis, we introduce a nonuniform spatial filter, an adaptive recursive temporal filter, and a principled scheme for locally estimating the spatial blur. Our scheme is appropriate for antialiasing shading attributes that vary slowly over time. It works in a single rendering pass on commodity graphics hardware, and offers results that surpass 4x4 stratified supersampling in quality, at a fraction of the cost.

Robust reprojection methods for the resolution of the Gibbs phenomenon

The classical Gibbs phenomenon exhibited by global Fourier projections and interpolants can be resolved in smooth regions by reprojecting in a truncated Gegenbauer series, achieving high resolution recovery of the function up to the point of discontinuity. Unfortunately, due to the poor conditioning of the Gegenbauer polynomials, the method suffers both from numerical round-off error and the Runge phenomenon. In some cases the method fails to converge. Following the work in [D. Gottlieb, C.W. Shu, Atti Conv. Lincei 147 (1998) 39–48], a more general framework for reprojection methods is introduced here. From this insight we propose an additional requirement on the reprojection basis which ameliorates the limitations of the Gegenbauer reconstruction. The new robust Gibbs complementary basis yields a reliable exponentially accurate resolution of the Gibbs phenomenon up to the discontinuities.

Geometrically valid pixel reprojection methods for novel view synthesis

Conventional methods for scene visualization involve 3-D model reconstruction and direct rendering of the model. More recently, however, there has been an increasing interest in an alternative means for novel view synthesis, namely image-based rendering. It refers to a collection of techniques for creating new views directly from a set of input images; these images act as the scene `model'. This paper describes in detail a particular subset of image-based rendering techniques, which we refer to as geometrically valid pixel reprojection techniques. These techniques are based on established bilinear and trilinear image constraints in the forms of the fundamental matrix and trilinear tensor, respectively. We also describe an image-based rendering technique that uses as input a collection of cylindrical panoramic images.

Study of reprojection methods in terms of their resolution loss and sampling errors

Two reprojection methods are studied to their resolution loss and sampling errors. The methods are area weighted convolution (AWC), and Gaussian pixel convolution (GPC). Modulation transfer function (MTF) is used to evaluate the resolution loss, and the residual sum of squares (RSS) of the difference between the reprojected sinogram and a reference sinogram corresponding to infinite sampling is used to assess the sampling errors. The resolution loss is found to be determined by the reconstruction filter, the linear interpolation in the backprojection, and the convolution kernel. Sampling errors are found to be angle-dependent, and the angular dependency is more pronounced for the GPC. To avoid significant sampling errors, the width of the convolution kernel needs to be two times larger than the pixel distance. Large sub-binning size of the projection array leads to interpolation error, which is more pronounced for AWC than for GPC. For the GPC method, with pixel size twice the pixel distance, the sampling error can be greatly reduced. The sampling error can be reduced without additional resolution loss by using a smaller pixel distance.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Interactive display of volumetric data by Fast Fourier Projection

This article describes a new algorithm for reprojection of volumetric data, called Fast Fourier Projection (FFP), which is one to two orders of magnitude faster than conventional methods such as ray casting. The theoretical basis of the new method is developed in a unified mathematical framework encompassing slice imaging and conventional volumetric reprojection methods. Software implementation is discussed in detail. The article closes with an account of experience with a prototype FFP implementation, and applications of the technique in medical visualization.

A Computer Aided Diagnosis System Based on 3D Density Reprojection Methods

A Computer Aided Diagnosis System Based on 3D Density Reprojection Methods

Errors in Reprojection Methods in Computenzed Tomography

Iterative tomographic reconstruction methods have been developed which can enforce various physical constraints on the reconstructed image. An integral part of most of these methods is the repro. jection of the reconstructed image. These estimated projections are compared to the original projection data and modified according to some criteria based on a priori constraints. In this paper, the errors generated by such reprojection schemes are investigated. Bounds for these errors are derived under simple signal energy assumptions and using probabilistic assumptions on the distribution of discontinuities. These bounds can be used in the enforcement of constraints, in the determination of convergence of the iterative methods, and in the detection of artifacts.