The interpretation of colour images is presented as an inverse problem in which a mapping is sought between image colour vectors and the physiological parameters characterizing a tissue. To ensure the necessary one-to-one correspondence between the image colours and the parameters, the mapping must be unique. This can be established through testing the sign of the determinant of the Jacobian ma...

This paper develops information geometric representations for nonlinear filters in continuous time. The posterior distribution associated with an abstract nonlinear filtering problem is shown to satisfy a stochastic differential equation on a Hilbert information manifold. This supports the Fisher metric as a pseudo-Riemannian metric. Flows of Shannon information are shown to be connected with t...

Edge detection is important both for its practical applications to computer vision as well as its relationship to early processing in the visual cortex. We describe experiments in which the rescaling backpropagalion learning algorithm was used to learn sets of linear filters for the task of determining the orientation and location of edges to sub-pixel accuracy. A model of edge formation was us...

This paper proposes an image quality metric (IQM) using compressive sensing (CS) and a filter set consisting of derivative and Gabor filters. In this paper, compressive sensing that is used for acquiring a sparse or compressible signal with a small number of measurements is used for measuring the quality between the reference and distorted images. However, an image is generally neither sparse n...

In this paper, we present nonlinear Bayesian filters for training recurrent neural networks with a special emphasis on a novel, more accurate, derivative-free member of the approximate Bayesian filter family called the cubature Kalman filter. We discuss the theory of Bayesian filters, which is rooted in the state-space modeling of the dynamic system in question and the linear estimation princip...

SUMMARY The design of the finite impulse response (FIR) notch filter with controlled null width is expressed as a derivatively contrained quadratic optimization problem. The problem is transformed into an un-constrained one by choosing a null matrix orthogonal to the derivative constraint matrix. In this paper, subband decomposition using wavelet filters is employed to construct the null matrix...

We try to answer the following set of questions: ``Is it possible to design step edge detection filters given the desired response to an input step edge signal?''; ``The method extends easily to two dimensions?'' and ``Do we improve edge detection using this method?''. Answers to these questions are given by formulating the step edge detection problem in terms of a linear first kind Fredholm in...

We address the problem of signal denoising and pattern recognition in processing batch-mode time-series data by combining linear time-invariant filters, orthogonal multiresolution representations, sparsity-based methods. propose a novel approach to designing higher-order zero-phase low-pass, high-pass, band-pass infinite impulse response filters as matrices, using spectral transformation state-...

Intrinsic image extraction has long been an important task for computer vision applications. However, this task is nontrivial at all because it is an ill-conditioned problem. The technique proposed in this paper uses one single image to achieve the purpose. The proposed approach first convolves the input image with a prescribed set of derivative filters. The pixels of the derivative images are ...

Steerable filters are a valuable tool for various low-level vision tasks. In this paper we address steerable filters for rotations in three dimensions. For two dimensions the theory is well developed. It is common to compute higher order expansions of certain type of filters and steer them according to their maximal response. The simplicity in 2D is due to the Fourier theory: the irreducible su...