Detection of edges from projections

Srinivasa, Narayan; Ramakrishnan, K. R.; Rajgopal, K.

doi:10.1109/42.126913

Cited by 39 publications

(22 citation statements)

References 17 publications

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“…(27) and (31) into Eq. (25), we obtain the following DBP formula of the derivative object function along the radial direction in the equidistant fan-beam geometry,…”

Section: A Reconstruction Of Derivative Object Function With Dbpmentioning

confidence: 99%

“…28,29 For example, the Laplacian for edge detection/enhancement has played an important role in contour outlining for area/volume measurement, feature extraction for image registration/fusion, and segmentation for image understanding. [26][27][28][29] It is straightforward for us to understand that such edge detection/enhancement filtering may also be desirable in the clinical applications of interior tomography. Moreover, it is our opinion that a radial differential filtering, which is a local and linear operator for edge detection/enhancement, may provide the morphological information that is relevant for image analysis and characterization in clinical applications.…”

Section: Introductionmentioning

confidence: 99%

“…In the clinical applications of conventional tomography, certain filtering for edge detection or enhancement, which is mathematically local, [24][25][26][27] may facilitate the tasks in image analysis and characterization to improve the accuracy and precision in computer aided diagnosis (CAD) and treatment planning in image-guided radiation therapy. 28,29 For example, the Laplacian for edge detection/enhancement has played an important role in contour outlining for area/volume measurement, feature extraction for image registration/fusion, and segmentation for image understanding.…”

Section: Introductionmentioning

confidence: 99%

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Radial differential interior tomography and its image reconstruction with differentiated backprojection and projection onto convex sets

Tang

2013

Medical Physics

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Purpose: Interior tomography has been recognized as one of the most effective approaches in computed tomography (CT) to reduce radiation dose rendered to patients. In this work, the authors propose and evaluate an imaging method of radial differential interior tomography. Methods: In interior tomography, an x-ray beam is collimated to only irradiate the region of interest (ROI) with suspected lesions while the surrounding area/volume of normal tissues/organs is spared. In the proposed imaging method of radial differential interior tomography, the outcome is a ROI image that has gone through a radial differential filtering. The image reconstruction algorithm for the radial differential interior tomography is kept in the fashion of differentiated backprojection and projection onto convex sets, but the required a priori knowledge in a small round area becomes zero and may be more readily available in practice. Results: Using the projection data simulated by computer and acquired by CT scanner, the authors evaluate and verify the performance of the proposed radial differential interior tomography method and its associated image reconstruction algorithm. The preliminary results show that the proposed imaging method can generate an image that is the radial differentiation of a conventional tomographic image and is robust over noise that inevitably exist in practice. Conclusions: It is believed that the proposed imaging method may find its utility in advanced clinical applications wherein a ROI-based image processing and analysis is required for lesion visualization, characterization, and diagnosis.

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“…(27) and (31) into Eq. (25), we obtain the following DBP formula of the derivative object function along the radial direction in the equidistant fan-beam geometry,…”

Section: A Reconstruction Of Derivative Object Function With Dbpmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Radial differential interior tomography and its image reconstruction with differentiated backprojection and projection onto convex sets

Tang

2013

Medical Physics

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“…In this section we present some sample reconstructions and performance plots for which we use the Initial Guess algorithm for generating a starting point to the nonlinear optimization (3). These experiments aim to show that the Initial Guess Algorithm does indeed provide us with a starting guess that in the great majority of the cases is near the global optimum.…”

Section: Initial Guess Algorithmmentioning

confidence: 99%

Reconstructing Binary Polygonal Objects from Projections: A Statistical View

Milanfar

1994

Graphical Models and Image Processing

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Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. AbstractIn many applications of tomography, the fundamental quantities of interest in an image are geometric ones. In these instances, pixel based signal processing and reconstruction is at best inefficient, and at worst, nonrobust in its use of the available tomographic data. Classical reconstruction techniques such as Filtered Back-Projection tend to produce spurious features when data is sparse and noisy; and these "ghosts" further complicate the process of extracting what is often a limited number of rather simple geometric features. In this paper we present a framework that, in its most general form, is a statistically optimal technique for the extraction of specific geometric features of objects directly from the noisy projection data. We focus on the tomographic reconstruction of binary polygonal objects from sparse and noisy data. In our setting, the tomographic reconstruction problem is essentially formulated as a (finite dimensional) parameter estimation problem. In particular, the vertices of binary polygons are used as their defining parameters. Under the assumption that the projection data are corrupted by Gaussian white noise, we use the Maximum Likelihood (ML) criterion, when the number of parameters is assumed known, and the Minimum Description Length (MDL) criterion for reconstruction when the number of parameters is not known. The resulting optimization problems are nonlinear and thus are plagued by numerous extraneous local extrema, making their solution far from trivial. In particular, proper initialization of any iterative technique is essential for good performance.To this end, we provide a novel method to construct a reliable yet simple initial guess for the solution. This procedure is based on the estimated moments of the object, which may be conveniently obtained directly from the noisy projection data.2

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“…The CBP reconstruction, though fast, is not suitable for imaging problems where the projection data are incomplete (limited angle and/or truncated projections) [2,7] or noisy and where the fundamental interest is not in the actual pixel values themselves, but rather in something that is derived from these, such as averages, boundaries [4] etc. These problems are encountered in many applications in medicine, non-destructive testing, oceanography and surveillance.…”

Section: Introductionmentioning

confidence: 99%

Using Natural Wavelet Bases and Multiscale Stochastic Models for Tomographic Reconstruction

Bhatia¹,

Karl²,

Willsky³

1993

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We use a multiscale natural pixel type representation of an object, originally developed for incomplete data problems, to construct nearly orthonormal basis functions. The coefficients of expansion of an object in these basis functions are obtained as the 1-D wavelet transform of the (strip integral) projections of the object. This enables us to formulate a multiscale tomographic reconstruction technique wherein the object is reconstructed at multiple scales or resolutions. A complete reconstruction is obtained by combining the reconstructions at different scales. The nearly orthonormal behavior of the basis functions results in a system matrix, relating the input (the object coefficients) and the output (the projection data), which is extremely sparse. The system matrix, in addition to being sparse, is well-conditioned and has a symmetric block-Toeplitz structure if the angular projections are uniformly spaced between 00 and 1800°. Fast inversion algorithms exist for these matrices. The multiscale reconstruction technique can find applications in object feature recognition directly from projection data, tackling ill-posed imaging problems where the projection data are incomplete and/or noisy, and construction of multiscale stochastic models for which fast estimation algorithms exist. In this paper, we include examples illustrating the above applications of our multiscale reconstruction technique.

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Detection of edges from projections

Cited by 39 publications

References 17 publications

Radial differential interior tomography and its image reconstruction with differentiated backprojection and projection onto convex sets

Radial differential interior tomography and its image reconstruction with differentiated backprojection and projection onto convex sets

Reconstructing Binary Polygonal Objects from Projections: A Statistical View

Using Natural Wavelet Bases and Multiscale Stochastic Models for Tomographic Reconstruction

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