Reconstruction from projections based on detection and estimation of objects--Parts I and II: Performance analysis and robustness analysis

Rossi, David J.; Willsky, Alan S.

doi:10.1109/tassp.1984.1164405

Cited by 108 publications

(54 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Finally, in low dose tomography the line integral observations may yield little more than shadow information [191, [18], [26], thus fitting into the silhouette framework above. Even when this is not the case, a preliminary step of projection support extraction coupled with object boundary estimation may be useful or desirable [21], [19]. This approach has proven particularly helpful in reflection tomography arising in laser range data [14].…”

Section: H(v) Z H(v/llvll)mentioning

confidence: 99%

Local tests for consistency of support hyperplane data

Karl

Kulkarni

Verghese³

et al. 1996

J Math Imaging Vis

View full text Add to dashboard Cite

Abstract. Support functions and samples of convex bodies in R ~ are studied with regard to conditions for their validity or consistency. Necessary and sufficient conditions for a function to be a support function are reviewed in a general setting. An apparently little known classical such result for the planar case due to Rademacher and based on a determinantal inequality is presented and a generalization to, arbitrary dimensions is developed. These conditions are global in the sense that they involve values of the support function at widely separated points. The corresponding discrete problem of determining the validity of a set of samples of a support function is treated. Conditions similar to the continuous inequality results are given for the consistency of a set of discrete support observations. These conditions are in terms of a series of local inequality tests involving only neighboring support samples. Our results serve to generalize existing planar conditions to arbitrary dimensions by providing a generalization of the notion of nearest neighbor for plane vectors which utilizes a simple positive cone condition on the respective support sample normals.

show abstract

Section: H(v) Z H(v/llvll)mentioning

confidence: 99%

Local tests for consistency of support hyperplane data

Karl

Kulkarni

Verghese³

et al. 1996

J Math Imaging Vis

View full text Add to dashboard Cite

show abstract

“…Of course, we may use these techniques even when the underlying object is not ellipsoidal, using the best fitting ellipsoid to obtain orientation and eccentricity information about an object. Such connections are explored in more detail in [11,12,14,18,21].…”

Section: Ellipsoid Projectionmentioning

confidence: 99%

“…In low dose tomography the line integral observations may yield little more than shadow information [11][12][13], thus fitting into the silhouette framework above. Even when this is not the case, a preliminary step of projection support extraction coupled with object boundary estimation may be useful or desirable [11,14]. This approach has proven particularly helpful in reflection tomography arising in laser range data [15].…”

Section: Introductionmentioning

confidence: 99%

Reconstructing Ellipsoids from Projections

Karl

1994

Graphical Models and Image Processing

View full text Add to dashboard Cite

In this paper we examine the problem of reconstructing a (possibly dynamic) ellipsoid from its (possibly inconsistent) orthogonal silhouette projections. We present a particularly convenient representation of ellipsoids as elements of the vector space of symmetric matrices. The relationship between an ellipsoid and its orthogonal projections in this representation is linear, unlike the standard parameterization based on semi-axis length and orientation. This representation is used to completely and simply characterize the solutions to the reconstruction problem. The representation also allows the straightforward inclusion of geometric constraints on the reconstructed ellipsoid in the form of inner and outer bounds on recovered ellipsoid shape. The inclusion of a dynamic model with natural behavior, such as stretching, shrinking, and rotation, is similarly straightforward in this framework and results in the possibility of dynamic ellipsoid estimation. For example, the linear reconstruction of a dynamic ellipsoid from a single lower-dimensional projection observed over time is possible. Numerical examples are provided to illustrate these points.

show abstract

“…Indeed, this issue is a major obstacle to the use of a statistically optimal, though nonlinear, approach such as given in (3) or (6). In this section we describe a method for using the projection data to directly compute an initial guess that is sufficiently close to the true global minimum as to, on average, result in convergence to it, or to a local minimum nearby.…”

Section: Algorithmic Aspects -Computing a Good Initial Guessmentioning

confidence: 99%

“…Other efforts in the parametric/geometric study of tomographic reconstruction have been carried out in the past. The work of Rossi and Willsky [6] and Prince and Willsky [7,8,9] has served as the starting point for this research effort. In the work of Rossi, the object was represented by a known profile, with only three geometric parameters; namely size, location, eccentricity, and orientation.…”

Section: Introductionmentioning

confidence: 99%

Reconstructing Binary Polygonal Objects from Projections: A Statistical View

Milanfar

1994

Graphical Models and Image Processing

View full text Add to dashboard Cite

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

show abstract

Reconstruction from projections based on detection and estimation of objects--Parts I and II: Performance analysis and robustness analysis

Cited by 108 publications

References 13 publications

Local tests for consistency of support hyperplane data

Local tests for consistency of support hyperplane data

Reconstructing Ellipsoids from Projections

Reconstructing Binary Polygonal Objects from Projections: A Statistical View

Contact Info

Product

Resources

About