Application of the Fisher-Rao Metric to Ellipse Detection

Maybank, Stephen J.

doi:10.1007/s11263-006-9033-z

Cited by 8 publications

(7 citation statements)

References 37 publications

(51 reference statements)

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“…Notice that this measure also depends on µ β , which was already computed in Equation (12). Therefore, denoting q = L + (1 − β)(m − L), the Rényi entropy is expressed by…”

Section: A Expressions For the Complex Wishart Distributionmentioning

confidence: 96%

Entropy-Based Statistical Analysis of PolSAR Data

Frery

Cintra

Nascimento

2013

IEEE Trans. Geosci. Remote Sensing

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Abstract-Images obtained from coherent illumination processes are contaminated with speckle noise, with polarimetric synthetic aperture radar (PolSAR) imagery as a prominent example. With an adequacy widely attested in the literature, the scaled complex Wishart distribution is an acceptable model for PolSAR data. In this perspective, we derive analytic expressions for the Shannon, Rényi, and restricted Tsallis entropies under this model. Relationships between the derived measures and the parameters of the scaled Wishart law (i.e., the equivalent number of looks and the covariance matrix) are discussed. In addition, we obtain the asymptotic variances of the Shannon and Rényi entropies when replacing distribution parameters by maximum likelihood estimators. As a consequence, confidence intervals based on these two entropies are also derived and proposed as new ways of capturing contrast. New hypothesis tests are additionally proposed using these results, and their performance is assessed using simulated and real data. In general terms, the test based on the Shannon entropy outperforms those based on Rényi's.

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“…Notice that this measure also depends on µ β , which was already computed in Equation (12). Therefore, denoting q = L + (1 − β)(m − L), the Rényi entropy is expressed by…”

Section: A Expressions For the Complex Wishart Distributionmentioning

confidence: 96%

Entropy-Based Statistical Analysis of PolSAR Data

Frery

Cintra

Nascimento

2013

IEEE Trans. Geosci. Remote Sensing

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“…Cover and Thomas (1991) describe the one dimensional version of the Fisher-Rao metric which is referred to as the Fisher information. Fisher-Rao metrics on the space of lines in the plane and the space of ellipses in the plane are described in Maybank (2004) and Maybank (2007) respectively. In both cases the measurements are points in the image.…”

Section: Fisher-rao Metricmentioning

confidence: 99%

A Fisher–Rao Metric for Curves Using the Information in Edges

Maybank

2015

J Math Imaging Vis

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Two curves which are close together in an image are indistinguishable given a measurement, in that there is no compelling reason to associate the measurement with one curve rather than the other. This observation is made quantitative using the parametric version of the Fisher-Rao metric. A probability density function for a measurement conditional on a curve is constructed. The distance between two curves is then defined to be the Fisher-Rao distance between the two conditional pdfs. A tractable approximation to the Fisher-Rao metric is obtained for the case in which the measurements are compound in that they consist of a point x and an angle α which specifies the direction of an edge at x. If the curves are circles or straight lines, then the approximating metric is generalized to take account of inlying and outlying measurements. An estimate is made of the number of measurements required for the accurate location of a circle in the presence of outliers. A Bayesian algorithm for circle detection is defined. The prior density for the algorithm is obtained from the Fisher-Rao metric. The algorithm is tested on images from the CASIA Iris Interval database.

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“…It is applied to the detection of image structures by Maybank (2004Maybank ( , 2005Maybank ( , 2007Maybank ( , 2008. See also Kanatani (1996), Section 14.4.…”

Section: Related Workmentioning

confidence: 99%

A Fisher-Rao Metric for Paracatadioptric Images of Lines

2012

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Abstract. In a central paracatadioptric imaging system a perspective camera takes an image of a scene reflected in a paraboloidal mirror. A 360• field of view is obtained, but the image is severely distorted. In particular, straight lines in the scene project to circles in the image. These distortions make it difficult to detect projected lines using standard image processing algorithms.The distortions are removed using a Fisher-Rao metric which is defined on the space of projected lines in the paracatadioptric image. The space of projected lines is divided into subsets such that on each subset the Fisher-Rao metric is closely approximated by the Euclidean metric. Each subset is sampled at the vertices of a square grid and values are assigned to the sampled points using an adaptation of the trace transform. The result is a set of digital images to which standard image processing algorithms can be applied. The effectiveness of this approach to line detection is illustrated using two algorithms, both of which are based on the Sobel edge operator. The task of line detection is reduced to the task of finding isolated peaks in a Sobel image. An experimental comparison is made between these two algorithms and third algorithm taken from the literature and based on the Hough transform.

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Application of the Fisher-Rao Metric to Ellipse Detection

Cited by 8 publications

References 37 publications

Entropy-Based Statistical Analysis of PolSAR Data

Entropy-Based Statistical Analysis of PolSAR Data

A Fisher–Rao Metric for Curves Using the Information in Edges

A Fisher-Rao Metric for Paracatadioptric Images of Lines

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