• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.597-605
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• 2020

In this article, we discuss the global uniqueness problem for the Radon transform. It is not sufficient for the global uniqueness for the Radon transform to assume that the Radon transform Rf for a function f absolutely converges on any hyperplane. It is also known that it is sufficient to assume that f ∈ L¹ for the global uniqueness to hold. There exists a big gap between the above two conditions, to fill which is our purpose in this paper. We shall give a better sufficient condition for the global uniqueness of the Radon transform.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1773-1781
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• 2018

The Radon transform introduced by J. Radon in 1917 is the integral transform which is widely applicable to tomography. Here we study the discrete version of the Radon transform. More precisely, when $C({\mathbb{Z}}^n_p)$ is the set of complex-valued functions on ${\mathbb{Z}}^n_p$. We completely determine the subset of $C({\mathbb{Z}}^n_p)$ whose elements can be recovered from its Radon transform on ${\mathbb{Z}}^n_p$.

• Proceedings of the IEEK Conference
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• summer
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• pp.274-275
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• 2004

The Hough transform has been used as a tool for line detection. The main idea of the Hough transform is to transform each pixel in the image individually into the parameter domain. In this way, the Hough transform converts a difficult global detection problem in the image domain into a more easily solved local peak detection problem in the parameter domain. In this paper, we show that the discrete Hough transform is identical to the discrete Radon transform. Thus, we can use the generalized Radon transform to handle more general parameterized curve types.

• Proceedings of the IEEK Conference
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• 1998.10a
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• pp.727-730
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• 1998

In this paper, we propose an implementation of an efficient parallel Radon transform on TMS320C80-based system. For an N$\times$N SAR image, we can obtain O(NM/p) of the conventional parallel Radon transform, by representing the projection patterns in Radon space variables instead of the image space variables, and pipelining the algorithm, where p is the number of processors and M is the number of projection angles. Also, we can reduce the time for the dynamic load distribution among the nodes and the communication overheads of accessing the global memories, by pipelining the memory and processing operations by using tripple buffer structure. Experimental results show an efficient parallel Radon transform of speedup Sp=3.9 and efficiency E=97.5% for 256$\times$256 image, when implemented on TMS320C80 composed of four parallel slave processors with three memory blocks.

• Journal of the Korea Society of Computer and Information
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• v.14 no.6
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• pp.65-71
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• 2009

The basic features in the indexing and retrieval of the image is used color, shape, and texture in traditional image retrieval method. We do not use these features and offers a new way. For content-based video indexing and retrieval, visual features used to measure the similarity of the geometric method is presented. This method is called the Radon transform. Without separation, this method is calculated based on the geometric distribution of image. In the experiment has a very good search results.

• Korean Journal of Remote Sensing
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• v.14 no.1
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• pp.17-36
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• 1998

The Radon transform has been widely used in various techniques of digital image processing such as the computerized topography, lineament analysis in a remotely sensed image, slant-stack processing of seismic data, and so on. Compared to the Fourier transform, the utility of two-dimensional convolutional or correlational properties of the Radon transform, however, has been underestimated. We show that the two-dimensional convolution and correlation is respectively reduced to be one-dimensional convolution and correlation with respect to ρ in the Radon space. Therefore, one can achieve a two dimensional filtering by applying a simple one-dimensional convolution in the Radon space followed by an inverse Radon transform. Tests of the approach using FIR filters are carried out specifically for enhancing the ship wake in a RADARSAT SAR image. The test results demonstrate that the two-dimensional filtering through the Radon transform effectively enhance the ship wake features as well as reducing sea speckle in the image. Although two-dimensional convolution and correlation through the Radon transform are not so much useful as those through the courier transform in views of efficiency and effectiveness, it can be utilized to improve the quality of a digitally processed output when the process should be accompanied by the Radon transform such as topography and lineament analysis of SAR image.

• Journal of KIISE:Computing Practices and Letters
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• v.14 no.3
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• pp.291-295
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• 2008

In this paper, we propose an input image reduction method to solve the problems of Radon transform which is a line structure analysis tool to correct a rotated object through a vision system. First we extract an object image removed background from the input image. Then we also select a reduced object image as a final input mage of Radon transform from the object image by considering slope. Finally we extract a rotated angle by using Radon transform with the final input image and correct the rotated object with the angle. In experimental results, we could improve the process time of about 64%, reduce the memory space of about 18% and make progress the line detection rate of about 18%.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.1
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• pp.29-37
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• 2017

A general optimal recovery problem is to approximate a value of a linear operator on a subset (class) in linear space from a value of another linear operator (called information), measured with an error in given metric. We use this formulation to investigate the classical computerized tomography problem of inversion of the noisy Radon transform.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.40 no.1
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• pp.124-129
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• 2003

A novel watermark registration method based on Radon transform for self-referencing watermark is presented. The novel method was successful in registering the watermark of the image that has undergone affine transformations and severe lossy compression, whereas the conventional method based on peak detection failed to register the watermark.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2009.01a
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• pp.450-455
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• 2009

Amplitude-only logarithmic Radon transform (ALR transform) for pattern matching is proposed. This method provides robustness for object translation, scaling, and rotation. An ALR image is invariant even if objects are translated in a picture. For the object scaling and rotation, the ALR image is merely translated. The objects are identified using a phase-only matched filter to the ALR image. The ratio of size, the difference of rotation angle, and the position between the two objects are detected. Our pattern matching procedure is described, herein, and its simulation is executed. We compare matching scores with the Fourier-Mellin transform, and the general phase-only matched filter.