The Experts below are selected from a list of 282 Experts worldwide ranked by ideXlab platform
David Taubman - One of the best experts on this subject based on the ideXlab platform.
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Orientation Adaptive Discrete Packet Wavelet Decomposition via Shifting Operators for Image Compression
14th International Conference on Image Analysis and Processing (ICIAP 2007), 2007Co-Authors: Stefano Andriani, David TaubmanAbstract:In this paper we present novel techniques to adapt conventional wavelet transforms to follow locally oriented features found in images. We introduce a shift operator before each step in a lifting implementation of the DWT. The best shifts are estimated by minimizing the high-pass coefficient energy and then used in both the prediction and update lifting steps. To approximate the asymptotically optimal rate-distortion performance of a piece-wise Regular Function more closely, we adopt a packet wavelet decomposition. Experimental results obtained integrating the proposed transform into the JPEG2000 codec show improvements in both visual and objective tests, allowing for a "better" representation of the edges at very-low rates. Very recently, some related ideas have been presented by other authors. The most distinctive features of this paper include a more flexible packet wavelet decomposition structure and a comparison between subband- and image-domain shifting operators.
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Spatially Continuous Orientation Adaptive Discrete Packet Wavelet Decomposition for Image Compression
2006 International Conference on Image Processing, 2006Co-Authors: Nagita Mehrseresht, David TaubmanAbstract:In this paper, we propose an orientation adaptive discrete wavelet transform (DWT) with perfect reconstruction. The proposed transform utilizes the lifting structure to effectively orient the 2D-DWT bases in the direction of local image features. A shifting operator is employed within each lifting step to align spatial geometric features along the vertical or horizontal directions. The proposed oriented transform generates a scalable representation for the image and the orientation information. To approximate the asymptotically optimal rate-distortion performance of a piecewise Regular Function more closely, we adopt a packet wavelet decomposition. The experimental results obtained by implementing the proposed transform in a JPEG2000 codec illustrate superior compression performance for the oriented transform with more than 2.5 dB improvement for highly oriented natural images. More importantly, even at the same PSNR, the proposed scheme reduces the visual appearance of the Gibbs-like artifacts significantly, considerably improving the visual quality of the reconstructed image.
Stefano Andriani - One of the best experts on this subject based on the ideXlab platform.
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Orientation Adaptive Discrete Packet Wavelet Decomposition via Shifting Operators for Image Compression
14th International Conference on Image Analysis and Processing (ICIAP 2007), 2007Co-Authors: Stefano Andriani, David TaubmanAbstract:In this paper we present novel techniques to adapt conventional wavelet transforms to follow locally oriented features found in images. We introduce a shift operator before each step in a lifting implementation of the DWT. The best shifts are estimated by minimizing the high-pass coefficient energy and then used in both the prediction and update lifting steps. To approximate the asymptotically optimal rate-distortion performance of a piece-wise Regular Function more closely, we adopt a packet wavelet decomposition. Experimental results obtained integrating the proposed transform into the JPEG2000 codec show improvements in both visual and objective tests, allowing for a "better" representation of the edges at very-low rates. Very recently, some related ideas have been presented by other authors. The most distinctive features of this paper include a more flexible packet wavelet decomposition structure and a comparison between subband- and image-domain shifting operators.
Thu Trang Lê - One of the best experts on this subject based on the ideXlab platform.
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Wavelet Operators and Multiplicative Observation Models—Application to SAR Image Time-Series Analysis
IEEE Transactions on Geoscience and Remote Sensing, 2016Co-Authors: Abdourrahmane Mahamane Atto, Emmanuel Trouvé, Jean-marie Nicolas, Thu Trang LêAbstract:This paper first provides statistical properties of wavelet operators when the observation model can be seen as the product of a deterministic piecewise Regular Function (signal) and a stationary random field (noise). This multiplicative observation model is analyzed in two standard frameworks by considering either: 1) a direct wavelet transform of the model; or 2) a log-transform of the model prior to wavelet decomposition. The paper shows that, in Framework 1, wavelet coefficients of the time series are affected by intricate correlation structures which blur signal singularities. Framework 2 is shown to be associated with a multiplicative (or geometric) wavelet transform, and the multiplicative interactions between wavelets and the model highlight both sparsity of signal changes near singularities (dominant coefficients) and decorrelation of speckle wavelet coefficients. This paper then derives that, for time series of synthetic aperture radar data, geometric wavelets represent a more intuitive and relevant framework for the analysis of smooth earth fields observed in the presence of speckle. From this analysis, this paper proposes a fast-and-concise geometric-wavelet-based method for joint change detection and Regularization of synthetic aperture radar image time series. In this method, geometric wavelet details are first computed with respect to the temporal axis in order to derive generalized-ratio change images from the time series. The changes are then enhanced, and speckle is attenuated by using spatial block sigmoid shrinkage. Finally, a Regularized time series is reconstructed from the sigmoid shrunken change images. Some applications highlight relevancy of the method for the analysis of SENTINEL-1A and TerraSAR-X image time series over Chamonix Mont Blanc.
Caterina Stoppato - One of the best experts on this subject based on the ideXlab platform.
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A local representation formula for quaternionic slice Regular Functions
arXiv: Complex Variables, 2020Co-Authors: Graziano Gentili, Caterina StoppatoAbstract:After their introduction in 2006, quaternionic slice Regular Functions have mostly been studied over domains that are symmetric with respect to the real axis. This choice was motivated by some foundational results published in 2009, such as the Representation Formula for axially symmetric domains. The present work studies slice Regular Functions over domains that are not axially symmetric, partly correcting the hypotheses of some previously published results. In particular, this work includes a Local Representation Formula valid without the symmetry hypothesis. Moreover, it determines a class of domains, called simple, having the following property: every slice Regular Function on a simple domain can be uniquely extended to the symmetric completion of its domain.
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A new series expansion for slice Regular Functions
Advances in Mathematics, 2012Co-Authors: Caterina StoppatoAbstract:Abstract A promising theory of quaternion-valued Functions of one quaternionic variable, now called slice Regular Functions, has been introduced by Gentili and Struppa in 2006. The basic examples of slice Regular Functions are the power series of type ∑ n ∈ N q n a n on their balls of convergence B ( 0 , R ) = { q ∈ H : | q | R } . Conversely, if f is a slice Regular Function on a domain Ω ⊆ H then it admits at each point q 0 ∈ Ω an expansion of type f ( q ) = ∑ n ∈ N ( q − q 0 ) ∗ n a n where ( q − q 0 ) ∗ n denotes the n th power of q − q 0 with respect to an appropriately defined multiplication ∗ . However, the information provided by such an expansion is somewhat limited by a fact: if q 0 does not lie on the real axis then the set of convergence of the series in the previous equation needs not be a Euclidean neighborhood of q 0 . We are now able to construct a new type of expansion that is not affected by this phenomenon: an expansion into series of polynomials valid in open subsets of the domain. Along with this construction, we present applications to the computation of the multiplicities of zeros and of partial derivatives.
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Zeros of Regular Functions and polynomials of a quaternionic variable
Michigan Mathematical Journal, 2008Co-Authors: Graziano Gentili, Caterina StoppatoAbstract:The fundamental elements of a new theory of Regular Functions of a quaternionic variable have been recently developed, following an idea of Cullen. In this paper we present a detailed study of the structure of the zero set of Cullen-Regular Functions. We prove that the zero sets of the Functions under investigation consist of isolated points or isolated 2-spheres, in the 4-dimensional real space of quaternions. Moreover, the zeros of a Regular Function can be factored by means of a non-standard product. The Fundamental Theorem of Algebra for quaternions, and the approach here adopted lead, in particular, to a deeper insight of the geometric and algebraic properties of the zero sets of polynomials with quaternionic coefficients.
Amedeo Altavilla - One of the best experts on this subject based on the ideXlab platform.
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*-exponential of slice-Regular Functions
arXiv: Complex Variables, 2018Co-Authors: Amedeo Altavilla, Chiara De FabritiisAbstract:According to [5] we define the $*$-exponential of a slice-Regular Function, which can be seen as a generalization of the complex exponential to quaternions. Explicit formulas for $\exp_*(f)$ are provided, also in terms of suitable sine and cosine Functions. We completely classify under which conditions the $*$-exponential of a Function is either slice-preserving or $\mathbb{C}_J$-preserving for some $J\in\mathbb{S}$ and show that $\exp_*(f)$ is never-vanishing. Sharp necessary and sufficient conditions are given in order that $\exp_*(f+g)=\exp_*(f)*\exp_*(g)$, finding an exceptional and unexpected case in which equality holds even if $f$ and $g$ do not commute. We also discuss the existence of a square root of a slice-preserving Regular Function, characterizing slice-preserving Functions (defined on the circularization of simply connected domains) which admit square roots. Square roots of this kind of Functions are used to provide a further formula for $\exp_{*}(f)$. A number of examples is given throughout the paper.
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s-Regular Functions which preserve a complex slice
Annali di Matematica Pura ed Applicata, 2018Co-Authors: Amedeo Altavilla, C. De FabritiisAbstract:We study global properties of quaternionic slice Regular Functions (also called s-Regular) defined on symmetric slice domains. In particular, thanks to new techniques and points of view, we can characterize the property of being one-slice preserving in terms of the projectivization of the vectorial part of the Function. We also define a “Hermitian” product on slice Regular Functions which gives us the possibility to express the $$*$$ -product of two s-Regular Functions in terms of the scalar product of suitable Functions constructed starting from f and g. Afterwards we are able to determine, under different assumptions, when the sum, the $$*$$ -product and the $$*$$ -conjugation of two slice Regular Functions preserve a complex slice. We also study when the $$*$$ -power of a slice Regular Function has this property or when it preserves all complex slices. To obtain these results, we prove two factorization theorems: in the first one, we are able to split a slice Regular Function into the product of two Functions: one keeping track of the zeroes and the other which is never vanishing; in the other one, we give necessary and sufficient conditions for a slice Regular Function (which preserves all complex slices) to be the symmetrized of a suitable slice Regular one.
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on the real differential of a slice Regular Function
Advances in Geometry, 2018Co-Authors: Amedeo AltavillaAbstract:In this paper we show that the real differential of any injective slice Regular Function is everywhere invertible. The result is a generalization of a theorem proved by G. Gentili, S. Salamon and C. Stoppato, and it is obtained thanks, in particular, to some new information regarding the first coefficients of a certain polynomial expansion for slice Regular Functions (called \textit{spherical expansion}), and to a new general result which says that the slice derivative of any injective slice Regular Function is different from zero. A useful tool proven in this paper is a new formula that relates slice and spherical derivatives of a slice Regular Function. Given a slice Regular Function, part of its singular set is described as the union of surfaces on which it results to be constant.
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Twistor interpretation of slice Regular Functions
Journal of Geometry and Physics, 2017Co-Authors: Amedeo AltavillaAbstract:Abstract Given a slice Regular Function f : Ω ⊂ H → H , with Ω ∩ R ≠ ∅ , it is possible to lift it to surfaces in the twistor space CP 3 of S 4 ≃ H ∪ { ∞ } (see Gentili et al., 2014). In this paper we show that the same result is true if one removes the hypothesis Ω ∩ R ≠ ∅ on the domain of the Function f . Moreover we find that if a surface S ⊂ CP 3 contains the image of the twistor lift of a slice Regular Function, then S has to be ruled by lines. Starting from these results we find all the projective classes of algebraic surfaces up to degree 3 in CP 3 that contain the lift of a slice Regular Function. In addition we extend and further explore the so-called twistor transform, that is a curve in G r 2 ( C 4 ) which, given a slice Regular Function, returns the arrangement of lines whose lift carries on. With the explicit expression of the twistor lift and of the twistor transform of a slice Regular Function we exhibit the set of slice Regular Functions whose twistor transform describes a rational line inside G r 2 ( C 4 ) , showing the role of slice Regular Functions not defined on R . At the end we study the twistor lift of a particular slice Regular Function not defined over the reals. This example shows the effectiveness of our approach and opens some questions.