Search results for "Spline"

ConformalALU: A Conformal Geometric Algebra Coprocessor for Medical Image Processing

2015

Medical imaging involves important computational geometric problems, such as image segmentation and analysis, shape approximation, three-dimensional (3D) modeling, and registration of volumetric data. In the last few years, Conformal Geometric Algebra (CGA), based on five-dimensional (5D) Clifford Algebra, is emerging as a new paradigm that offers simple and universal operators for the representation and solution of complex geometric problems. However, the widespread use of CGA has been so far hindered by its high dimensionality and computational complexity. This paper proposes a simplified formulation of the conformal geometric operations (reflections, rotations, translations, and uniform …

Color Correction for Image Stitching by Monotone Cubic Spline Interpolation

2015

This paper proposes a novel color correction scheme for image stitching where the color map transfer is modelled by a monotone Hermite cubic spline and smoothly propagated into the target image. A three-segments monotone cubic spline minimizing color distribution statistics and gradient differences with respect to both the source and target images is used. While the spline model can handle non-linear color maps, the minimization over the gradient differences limits strong alterations on the image structure. Adaptive heuristics are introduced to reduce the minimization search space and thus computational time. Experimental comparisons with respect to the state-of-the-art linear mapping model…

Defining and measuring the development of a country over time

2012

This paper introduces the concept of harmonic growth as an extended acceptation of the notion of development, and discusses its measurement via the Harmonic Growth Index (HGI). The growth is seen as harmonic when the behaviour of a benchmark time series, which here is a measure of wealth, such as per capita GDP, is followed by a similar pattern in socio-economic series. Unlike most widely used indicators in the literature, which take into account the measurement of development over a single time, HGI measures the degree to which a social indicator’s time series pattern matches with the GDP’s. The index is a function, ranging in [0, 1], of the coefficients of the uniform B-splines fitted to …

Cubic Local Splines on Non-uniform Grid

2015

In this chapter, two types of local cubic splines on non-uniform grids are described: 1. The simplest variation-diminishing splines and 2. The quasi-interpolating splines. The splines are computed by a simple fast computational algorithms that utilizes a relation between the splines and cubic interpolation polynomials. Those splines can serve as an efficient tool for real-time signal processing. As an input, they use either clean or noised arbitrarily-spaced samples. On the other hand, the capability to adapt the grid to the structure of an object and minimal requirements to the operating memory are great advantages for off-line processing of signals and multidimensional data arrays.

Progressive transmission of secured images with authentication using decompositions into monovariate functions

2014

International audience; We propose a progressive transmission approach of an image authenticated using an overlapping subimage that can be removed to restore the original image. Our approach is different from most visible water- marking approaches that allow one to later remove the watermark, because the mark is not directly introduced in the two-dimensional image space. Instead, it is rather applied to an equivalent monovariate representation of the image. Precisely, the approach is based on our progressive transmission approach that relies on a modified Kolmogorov spline network, and therefore inherits its advantages: resilience to packet losses during transmis- sion and support of hetero…

P-spline quantile regression: a new algorithm for smoothing parameter selection

An exponential spline interpolation for unequally spaced data points

1982

StalAge – An algorithm designed for construction of speleothem age models

2011

Abstract Here we present a new algorithm ( StalAge ), which is designed to construct speleothem age models. The algorithm uses U-series ages and their corresponding age uncertainty for modelling and also includes stratigraphic information in order to further constrain and improve the age model. StalAge is applicable to problematic datasets that include outliers, age inversions, hiatuses and large changes in growth rate. Manual selection of potentially inaccurate ages prior to application is not required. StalAge can be applied by the general, non-expert user and has no adjustable free parameters. This offers the highest degree of reproducibility and comparability of speleothem records from …

Spline-Based Wavelet Transforms

2018

The Lifting Scheme introduced in (Sweldens, Appl. Comput. Harmon. Anal. 3(2), 186–200 (1996) and Sweldens, SIAM J. Math. Anal. 29(2), 511–546 (1997).) [3, 4] is a method that constructs bi-orthogonal wavelet transforms of signals and provides their efficient implementation. The main feature of the lifting scheme is that all the constructions are derived directly in the spatial domain and therefore can be custom designed to more general and irregular settings such as non-uniformly spaced data samples and bounded intervals. In this chapter, we outline the lifting scheme and describe how to use the local quasi-interpolating splines, introduced in Chap. 6, for the construction of wavelet transf…

Periodic Discrete and Discrete-Time Splines

2018

Periodic discrete splines with different periods and spans are introduced in Sect. 3.4 of Volume I (Averbuch, Neittaanmaki and Zheludev, Spline and Spline Wavelet Methods with Applications to Signal and Image Processing, Springer, Berlin, 2014) [2]. In this chapter, we regard periodic discrete splines as a base for the design of periodic discrete-time wavelets, wavelet packets and wavelet frames. Therefore, only the discrete splines whose spans are 2 are outlined. These discrete splines are linear combinations of the discrete B-splines. So also, the so-called discrete-time splines are discussed in the chapter that are linear combinations of the discrete-time B-splines. The discrete-time B-s…