988 research outputs found

    PIMs and invariant parts for shape recognition

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    Journal ArticleWe present completely new very powerful solutions t o two fundamental problems central to computer vision. 1. Given data sets representing C objects to be stored in a database, and given a new data set for an object, determine the object in the database that is most like the object measured. We solve this problem through use of PIMs ("Polynomial Interpolated Measures"), which, is a new representation integrating implicit polynomial curves and surfaces, explicit polynomials, and discrete data sets which may be sparse. The method provides high accuracy at low computational cost. 2. Given noisy 20 data along a curve (or 30 data along a surface), decompose the data into patches such that new data taken along affine transformation-s or Eucladean transformations of the curve (or surface) can be decomposed into corresponding patches. Then recognition of complex or partially occluded objects can be done in terms of invariantly determined patches. We briefly outline a low computational cost image-database indexing-system based on this representation for objects having complex shape-geometry

    Algebraic Curve Fitting Support Vector Machines

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    An algebraic curve is defined as the zero set of a multivariate polynomial. We consider the problem of fitting an algebraic curve to a set of vectors given an additional set of vectors labelled as interior or exterior to the curve. The problem of fitting a linear curve in this way is shown to lend itself to a support vector representation, allowing non-linear curves and high dimensional surfaces to be estimated using kernel functions. The approach is attractive due to the stability of solutions obtained, the range of functional forms made ossible (including polynomials), and the potential for applying well understood regularisation operators from the theory of Support Vector Machines

    Kernel Based Algebraic Curve Fitting

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    An algebraic curve is defined as the zero set of a multivariate polynomial. We consider the problem of fitting an algebraic curve to a set of vectors given an additional set of vectors labelled as interior or exterior to the curve. The problem of fitting a linear curve in this way is shown to lend itself to a support vector representation, allowing non-linear curves and high dimensional surfaces to be estimated using kernel functions. The approach is attractive due to the stability of solutions obtained, the range of functional forms made possible (including polynomials), and the potential for applying well understood regularisation operators from the theory of Support Vector Machines

    NEW ALGEBRAIC INVARIANTS OF IMPLICIT POLYNOMIALS FOR 3D OBJECT RECOGNITION

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    Abstract In this paper, we present a method for deriving the rotation invariants of 2 nd and 4 th degree implicit polynomials and we build a system for 3D object recognition using the derived invariants. Our results show that invariants derived in this paper are stable and the success of the recognition is high when the polynomial fit is successful

    Topologically faithful fitting of simple closed curves

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    Different approaches on the implementation of implicit polynomials in visual tracking /

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    Visual tracking has emerged as an important component of systems in several application areas including vision-based control, human-computer interfaces, surveillance, agricultural automation, medical imaging and visual reconstruction. The central challenge in visual tracking is to keep track of the pose and location of one or more objects through a sequence of frames. Implicit algebraic 2D curves and 3D surfaces are among the most powerful representations and have proven very useful in many model-based applications in the past two decades. With this approach, objects in 2D images are described by their silhouettes and then represented by 2D implicit polynomial curves. In our work, we tried different approaches in order to efficiently apply the powerful implicit algebraic 2D curve representation to the phenomenon of visual tracking. Through the proposed concepts and algorithms, we tried to reduce the computational burden of fitting algorithms. Besides showing the usage of this representation on boundary data simulations, use of the implicit polynomial as a representative of the target region is also experimented on real videos

    A wavelet based method for affine invariant 2D object recognition

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    Recognizing objects that have undergone certain viewing transformations is an important problem in the field of computer vision. Most current research has focused almost exclusively on single aspects of the problem, concentrating on a few geometric transformations and distortions. Probably, the most important one is the affine transformation which may be considered as an approximation to perspective transformation. Many algorithms were developed for this purpose. Most popular ones are Fourier descriptors and moment based methods. Another powerful tool to recognize affine transformed objects, is the invariants of implicit polynomials. These three methods are usually called as traditional methods. Wavelet-based affine invariant functions are recent contributions to the solution of the problem. This method is better at recognition and more robust to noise compared to other methods. These functions mostly rely on the object contour and undecimated wavelet transform. In this thesis, a technique is developed to recognize objects undergoing a general affine transformation. Affine invariant functions are used, based on on image projections and high-pass filtered images of objects at projection angles . Decimated Wavelet Transform is used instead of undecimated Wavelet Transform. We compared our method with the an another wavelet based affine invariant function, Khalil-Bayoumi and also with traditional methods

    Improving the stability of algebraic curves for applications

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    Journal ArticleAn algebraic curve is defined as the zero set of a polynomial in two variables. Algebraic curves are practical for modeling shapes much more complicated than conics or superquadrics. The main drawback in representing shapes by algebraic curves has been the lack of repeatability in fitting algebraic curves to data. Usually, arguments against using algebraic curves involve references to mathematicians Wilkinson (see [1, ch. 7] and Runge (see [3, ch. 4]). The first goal of this article is to understand the stability issue of algebraic curve fitting. Then a fitting method based on ridge regression and restricting the representation to well behaved subsets of polynomials is proposed, and its properties are investigated. The fitting algorithm is of sufficient stability for very fast position-invariant shape recognition, position estimation, and shape tracking, based on invariants and new representations. Among appropriate applications are shape-based indexing into image databases
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