Proceedings of Sixth International Conference on Document Analysis and Recognition
This paper presents a new model based document image segmentation scheme that uses XML-DTDs (eXte... more This paper presents a new model based document image segmentation scheme that uses XML-DTDs (eXtensible Mark-up Language-Document Type Definition). Given a document image, the algorithm has the ability to select the appropriate model. A new wavelet based tool has been designed for distinguishing text from non-text regions and characterization of font sizes. Our model based analysis scheme makes use of this tool for identifying the logical components of a document image.
Discrete Wavelet Transform (DWT) and its generalization, Wavelet Packets (WPs) have acquired cent... more Discrete Wavelet Transform (DWT) and its generalization, Wavelet Packets (WPs) have acquired central position for signal representation. DWT provides good compaction for low pass signals only. On the other hand WPs offers good approximation property for arbitrary signal but the associated computational cost of finding an optimal WP basis is quite high. In this paper, we introduce a signal conditioning based modulated wavelet transform. The proposed transformation provides better approximation performance than that offered by DWT for signal with arbitrary spectra, which can be used in signal approximation, compression, de-noising etc. The proposed transformation in its original form requires computation of signal parity information for which a fast algorithm is proposed. The proposed transform can be implemented efficiently similar to wavelet transform. Simulation results to demonstrate the improved approximation performance are also provided.
Fourier theory is a popular tool for analyzing various signals and interpreting their spectral co... more Fourier theory is a popular tool for analyzing various signals and interpreting their spectral contents. It finds applications in a wide variety of subject areas. However, some of the popular signals, such as sinusoidal signals, Dirac delta, signum, and unit step, fail to have a convergent Fourier representation (FR) in the conventional sense. Hence, it becomes imperative to utilize the distribution theory to understand and build a suitable representation for these signals. The signal processing and communication engineering literature does not explain these concepts clearly. As a result, many of the concepts of FR for signals that do not conform to the conventional derivations remain obscure to researchers. We attempt to bridge this gap and provide a comprehensive explanation regarding the existence of FR. Further, we have proposed a new linear space of Gauss--Schwartz (GS) functions and corresponding tempered superexponential (TSE) distributions. It is shown that the Fourier trans...
In this paper we propose and study few applications of the base structured categories X ⋊ F C, CF... more In this paper we propose and study few applications of the base structured categories X ⋊ F C, CF , X ⋊ F C and CF. First we show classic transformation groupoid X/ /G simply being a base-structured category GF. Then using permutation action on a finite set, we introduce the notion of a hierarchy of base structured categories [(X 2a ⋊ F2a B 2a) ∐ (X 2b ⋊ F 2b B 2b) ∐ ...] ⋊ F1 B 1 that models local and global structures as a special case of composite Grothendieck fibration. Further utilizing the existing notion of transformation double category (X 1 ⋊ F1 B 1)/ /2G, we demonstrate that a hierarchy of bases naturally leads one from 2-groups to n-category theory. Finally we prove that every classic Klein geometry is the Grothendieck completion (G = X ⋊ F H) of F : H F − → Man ∞ U − → Set. This is generalized to propose a set-theoretic definition of a groupoid geometry (G, B) (originally conceived by Ehresmann through transport and later by Leyton using transfer) with a principal groupoid G = X ⋊ B and geometry space X = G/B; which is essentially same as G = X ⋊ F B or precisely the completion of F : B F
In search of a real three-dimensional, normed, associative, division algebra, Hamilton discovered... more In search of a real three-dimensional, normed, associative, division algebra, Hamilton discovered quaternions that form a non-commutative division algebra of quadruples. Later works showed that there are only four real division algebras with 1, 2, 4, or 8 dimensions. This work overcomes this limitation and introduces generalized hypercomplex numbers of all dimensions that are extensions of the traditional complex numbers. The space of these numbers forms non-distributive normed division algebra that is extendable to all finite dimensions. To obtain these extensions, we defined a unified multiplication, designated as scaling and rotative multiplication, fully compatible with the existing multiplication. Therefore, these numbers and the corresponding algebras reduce to distributive normed algebras for dimensions 1 and 2. Thus, this work presents a generalization of $\mathbb{C}$ in higher dimensions along with interesting insights into the geometry of the vectors in the corresponding s...
Fourier theory is the backbone of the area of Signal Processing (SP) and Communication Engineerin... more Fourier theory is the backbone of the area of Signal Processing (SP) and Communication Engineering. However, Fourier series (FS) or Fourier transform (FT) do not exist for some signals that fail to fulfill a predefined set of Dirichlet conditions (DCs). We note a subtle gap in the explanation of these conditions as available in the popular signal processing literature. They lack a certain degree of explanation essential for the proper understanding of the same. For example, the original second Dirichlet condition is the requirement of bounded variations over one time period for the convergence of Fourier Series, where there can be at most infinite but countable number of maxima and minima, and at most infinite but countable number of discontinuities of finite magnitude. However, a large body of the literature replaces this statement with the requirements of finite number of maxima and minima over one time period, and finite number of discontinuities. The latter incorrectly disqualif...
It is a challenging task to extract the best of both worlds by combining the spatial characterist... more It is a challenging task to extract the best of both worlds by combining the spatial characteristics of a visible image and the spectral content of an infrared image. In this work, we propose a spatially constrained adversarial autoencoder that extracts deep features from the infrared and visible images to obtain a more exhaustive and global representation. In this paper, we propose a residual autoencoder architecture, regularised by a residual adversarial network, to generate a more realistic fused image. The residual module serves as primary building for the encoder, decoder and adversarial network, as an add on the symmetric skip connections perform the functionality of embedding the spatial characteristics directly from the initial layers of encoder structure to the decoder part of the network. The spectral information in the infrared image is incorporated by adding the feature maps over several layers in the encoder part of the fusion structure, which makes inference on both th...
In this paper, we propose algorithms which preserve energy in empirical mode decomposition (EMD),... more In this paper, we propose algorithms which preserve energy in empirical mode decomposition (EMD), generating finite $n$ number of band limited Intrinsic Mode Functions (IMFs). In the first energy preserving EMD (EPEMD) algorithm, a signal is decomposed into linearly independent (LI), non orthogonal yet energy preserving (LINOEP) IMFs and residue (EPIMFs). It is shown that a vector in an inner product space can be represented as a sum of LI and non orthogonal vectors in such a way that Parseval's type property is satisfied. From the set of $n$ IMFs, through Gram-Schmidt orthogonalization method (GSOM), $n!$ set of orthogonal functions can be obtained. In the second algorithm, we show that if the orthogonalization process proceeds from lowest frequency IMF to highest frequency IMF, then the GSOM yields functions which preserve the properties of IMFs and the energy of a signal. With the Hilbert transform, these IMFs yield instantaneous frequencies and amplitudes as functions of tim...
In this paper we propose and lay the foundations of a functorial framework for representing signa... more In this paper we propose and lay the foundations of a functorial framework for representing signals. By incorporating additional category-theoretic relative and generative perspective alongside the classic set-theoretic measure theory the fundamental concepts of redundancy, compression are formulated in a novel authentic arrow-theoretic way. The existing classic framework representing a signal as a vector of appropriate linear space is shown as a special case of the proposed framework. Next in the context of signal-spaces as a categories we study the various covariant and contravariant forms of $L^0$ and $L^2$ functors using categories of measurable or measure spaces and their opposites involving Boolean and measure algebras along with partial extension. Finally we contribute a novel definition of intra-signal redundancy using general concept of isomorphism arrow in a category covering the translation case and others as special cases. Through category-theory we provide a simple yet ...
In this paper we study categories $(F,\mathbf{C},\mathbf{D})$ and $(\mathbb{F},\mathbf{C},\mathbf... more In this paper we study categories $(F,\mathbf{C},\mathbf{D})$ and $(\mathbb{F},\mathbf{C},\mathbf{Set})$ and prove them to be fibred on $\mathbf{C}$. Then we examine Grothendieck construction in the context of an ordinary functor $F: \mathbf{C} \rightarrow \mathbf{D}$ through the concept of trivial categorification, using an appropriate functor $\mathbf{F}: \mathbf{C} \xrightarrow{F} \mathbf{D} \xrightarrow{I} \mathbf{Cat}$ to construct $\int_{\mathbf{C}^{op}} \bar{\mathbf{F}}$. This category characterizes a functor as an abstract right category action while its dual $\mathcal{X} \rtimes_{\mathbf{F}} \mathbf{C}$ or $(\int_{\mathbf{C}^{op}} \bar{\mathbf{F}})^{op}$ characterizes a functor as an abstract left category action. Similarly using $\mathbb{F}: \mathbf{C} \xrightarrow{F} \mathbf{D} \xrightarrow{U} \mathbf{Set}$ we define $\mathcal{X} \rtimes_{\mathbb{F}} \mathbf{C}$ and ${\int_{\mathbf{C}^{op}} \bar{\mathbb{F}}}$ as categories denoting concrete left and right actions of $\mat...
Proceedings. Mathematical, physical, and engineering sciences, 2017
for many decades, there has been a general perception in the literature that Fourier methods are ... more for many decades, there has been a general perception in the literature that Fourier methods are not suitable for the analysis of nonlinear and non-stationary data. In this paper, we propose a novel and adaptive Fourier decomposition method (FDM), based on the Fourier theory, and demonstrate its efficacy for the analysis of nonlinear and non-stationary time series. The proposed FDM decomposes any data into a small number of 'Fourier intrinsic band functions' (FIBFs). The FDM presents a generalized Fourier expansion with variable amplitudes and variable frequencies of a time series by the Fourier method itself. We propose an idea of zero-phase filter bank-based multivariate FDM (MFDM), for the analysis of multivariate nonlinear and non-stationary time series, using the FDM. We also present an algorithm to obtain cut-off frequencies for MFDM. The proposed MFDM generates a finite number of band-limited multivariate FIBFs (MFIBFs). The MFDM preserves some intrinsic physical prop...
Exact Least Squares Algorithm for Signal Matched Synthesis Filter Bank: Part II
In the companion paper, we proposed a concept of signal matched whitening filter bank and develop... more In the companion paper, we proposed a concept of signal matched whitening filter bank and developed a time and order recursive, fast least squares algorithm for the same. Objective of part II of the paper is two fold: first is to define a concept of signal matched synthesis filter bank, hence combining definitions of part I and part II we obtain a filter bank matched to a given signal. We also develop a fast time and order recursive, least squares algorithm for obtaining the same. The synthesis filters, obtained here, reconstruct the given signal only and not every signal from the finite energy signal space (i.e. belonging to L^2(R)), as is usually done. The recursions, so obtained, result in a lattice-like structure. Since the filter parameters are not directly available, we also present an order recursive algorithm for the computation of signal matched synthesis filter bank coefficients from the lattice parameters. The second objective is to explore the possibility of using synthe...
We test for stochastic long-memory behavior in the returns series of currency rates for eighteen ... more We test for stochastic long-memory behavior in the returns series of currency rates for eighteen industrial countries using a semiparametric fractional estimation method. A sensitivity analysis is also carried out to analyze the temporal stability of the longmemory parameter. Contrary to the findings of some previous studies alluding to the presence of long memory in major currency rates, our evidence provides wide support to the martingale model (and therefore for foreign exchange market efficiency) for our broader sample of foreign currency rates. Any inference of long-range dependence is fragile, especially for the major currency rates. However, long-memory dynamics are found in a small number of secondary (nonmajor) currency rates.
This paper proposes a new method of estimating both biorthogonal compactly supported as well as s... more This paper proposes a new method of estimating both biorthogonal compactly supported as well as semi-orthogonal infinitely/compactly supported wavelet from a given signal. The method is based on maximizing projection of the given signal onto successive scaling subspace. This results in minimization of energy of signal in the wavelet subspace. The idea used to estimate analysis wavelet filter is similar to a sharpening filter used in image enhancement. First, a new method is proposed that helps in the design of 2-band FIR biorthogonal perfect reconstruction filter bank from a given signal. This leads to the design of biorthogonal compactly supported wavelet. It is also shown that a wavelet with desired support as well as desired number of vanishing moments can be designed with the proposed method. Next, a method is proposed to design semi-orthogonal wavelets that are usually infinitely supported wavelets. Here, corresponding to FIR analysis filters, the resulting synthesis filters are IIR filters that satisfy the property of perfect reconstruction.
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Papers by Shiv Joshi