Reconstruction is prerequisite whenever a discrete signal needs to be resampled as a result of transformation such as texture mapping, image manipulation, volume slicing. and rendering. We present a new method for the characterization and measurement of reconstruction error in spatial domain. Our method uses the Classical Shannon's Sampling Theorem as a basis to develop error bounds. We use this formulation to provide, for the first time, an efficient way to guarantee an error bound at every point by varying the size of the reconstruction filter. We go further to support position-adaptive reconstruction and data-adaptive reconstruction which adjust filter size to the location of reconstruction point and to the data values in its vicinity. We demonstrate the effectiveness of our methods with 1D signals, 2D signals (images), and 3D signals (volumes) . 1. Introduction Reconstruction is the process of recovering a continuous function from a set of samples. It is one of the fun...

Super-resolution reconstruction proposes a fusion of several low-quality images into one higher quality result with better optical resolution. Classic super-resolution techniques strongly rely on the availability of accurate motion estimation for this fusion task. When the motion is estimated inaccurately, as often happens for nonglobal motion fields, annoying artifacts appear in the super-resolved outcome. Encouraged by recent developments on the video denoising problem, where state-of-the-art algorithms are formed with no explicit motion estimation, we seek a super-resolution algorithm of similar nature that will allow processing sequences with general motion patterns. In this paper, we base our solution on the Nonlocal-Means (NLM) algorithm. We show how this denoising method is generalized to become a relatively simple super-resolution algorithm with no explicit motion estimation. Results on several test movies show that the proposed method is very successful in providing super-resolution on general sequences.

The main contributions of this work are summarised as follows: A flexible and low-cost object modelling framework, with rendering methods, for intermixing discrete and continuous volume data. Image-swept volumes: A new modelling paradigm in which attribute fields of volume objects are defined by sweeping discrete image or volume templates along arbitrary trajectories. A projection-based texture mapping method for volume objects. A method for rendering Bezier volumes and free-form deformations of volume objects. vlib: A volume graphics API, including detailed design and implementation details. The field-based modelling framework addresses the limitations of using discrete data for representing volume objects. It not only results in very high quality images (with shadows, reflection and refraction) while supporting "traditional" volume graphics, which we demonstrate using several examples, but also it frequently reduces the significant memory overhead that is normally associated

Reconstruction is imperative whenever an image needs to be resampled as a result of transformation such as an affine or perspective transform, or texture mapping.

Reconstruction is imperative whenever an image or a volume needs to be resampled as a result of an affine or perspective transformation, texture mapping, or volume rendering. We present a new method for the characterization and measurement of reconstruction error. Our method, based on spatial domain error analysis, uses approximation theory to develop error bounds. We provide, for the first time, an efficient way to guarantee an error bound at every point by varying the filter size. We go further to support position-adaptive and data-adaptive reconstruction which adjust filter size to the location of reconstruction and the data in its vicinity. We demonstrate the effectiveness of our methods with suitable 2D and 3D examples.

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This paper deals with some approximations by the generalized Shannon sampling series, which are defined by the Blackman-Harris (or cosine-sum) window functions. In the case of certain (m + 1)-term cosine-sum window functions the order of approximation can be estimated via the 2m-th modulus of continuity. Some choices of parameters in Blackman-Harris window function generate interpolating generalized Shannon sampling series. Copyright line will be provided by the publisher 1