Craig M. Shakarji

RECIST versus volume measurement in medical CT using ellipsoids of known size.

Two hundred eighty three uniaxial ellipsoids with sizes from 4 mm to 11 mm were measured with a coordinate measuring matching (CMM) and also scanned using a medical computed tomography (CT) machine. Their volumes were determined by counting voxels over a threshold, as well as using equivalent volumes from the length given by the RECIST 1.1 criterion (Response Evaluation Criteria in Solid Tumors). The volumetric measurements yield an order of magnitude reduction in residuals compared to the CMM measurements than the residuals of the RECIST measurements also compared to the CMM measurements.

Development of tools for measuring the performance of computer assisted orthopaedic hip surgery systems

In the late seventies a sensor was invented, which could track the movement of athlete body parts. In the early eighties an improved version of this sensor was introduced, by a group of NIST researchers, for the calibration and the performance testing of industrial robots. In the late eighties people experimented with the use of these sensors for human brain operations and in the early nineties these sensors were introduced to orthopaedic operations and the field of Computer Assisted Orthopaedic Surgery (CAOS) was born. Although significant progress has been made in the design and use of these sensors for medical applications, there are still sources of accuracy errors that must be addressed. This paper describes our work on the development of tools for the calibration and performance testing of CAOS systems, which can be used inside operating rooms.

On the Enduring Appeal of Least-Squares Fitting in Computational Coordinate Metrology

The vast majority of points collected with coordinate measuring machines are not used in isolation; rather, collections of these points are associated with geometric features through fitting routines. In manufacturing applications, there are two fundamental questions that persist about the efficacy of this fitting—first, do the points collected adequately represent the surface under inspection; and second, does the association of substitute (fitted) geometry with the points meet criteria consistent with the standardized geometric specification of the product. This paper addresses the second question for least-squares fitting both as a historical survey of past and current practices, and as a harbinger of the influence of new specification criteria under consideration for international standardization. It also touches upon a set of new issues posed by the international standardization on the first question as related to sampling and least-squares fitting.

Theory and Algorithms for Weighted Total Least-Squares Fitting of Lines, Planes, and Parallel Planes to Support Tolerancing Standards

We present the theory and algorithms for fitting a line, a plane, two parallel planes (corresponding to a slot or a slab), or many parallel planes in a total (orthogonal) least-squares sense to coordinate data that is weighted. Each of these problems is reduced to a simple 3 � 3 matrix eigenvalue/eigenvector problem or an equivalent singular value decomposition problem, which can be solved using reliable and readily available commercial software. These methods were numerically verified by comparing them with brute-force minimization searches. We demonstrate the need for such weighted total least-squares fitting in coordinate metrology to support new and emerging tolerancing standards, for instance, ISO 14405-1:2010. The widespread practice of unweighted fitting works well enough when point sampling is controlled and can be made uniform (e.g., using a discrete point contact coordinate measuring machine). However, we show by example that nonuniformly sampled points (arising from many new measurement technologies) coupled with unweighted least-squares fitting can lead to erroneous results. When needed, the algorithms presented also solve the unweighted cases simply by assigning the value one to each weight. We additionally prove convergence from the discrete to continuous cases of least-squares fitting as the point sampling becomes dense. [DOI: 10.1115/1.4024854]

Dimensional measurement traceability of 3D imaging data

This paper discusses the concept of metrological traceability to the International System of Units (SI) unit of length, the meter. We describe how metrological traceability is realized, give a recent example of the standardization of laser trackers, and discuss progress and challenges to the traceability of 3D imaging data.

Datum Planes Based on a Constrained L1 Norm

This paper has two major goals. First, we present an algorithm for establishing planar datums suitable for a default in tolerancing standards. The algorithm is based on a constrained minimization search based on the L1 (L1) norm after forming a convex surface from the original surface or sampled points. We prove that the problem reduces to a simple minimization search between the convex surface and its centroid. The data points in the discrete case do not need to have any corresponding weights provided with them, as appropriate weighting is part of the algorithm itself, thereby making the algorithm largely insensitive to nonuniformly sampled data points. Terse mathematica code is included for the reader. The code is sufficient for primary and secondary planar datum fitting as well as a 3-2-1 datum reference frame generation. The second goal of this paper is to compare this new method with several other possible means for establishing datum planes, ultimately showing several appealing characteristics of the proposed algorithm. Since both the International Organization for Standardization (ISO) and American Society of Mechanical Engineers (ASME) standardization efforts are actively working to establish datum plane definitions, the timing of such a study is opportune.

A Constrained L2 Based Algorithm for Standardized Planar Datum Establishment

For years (decades, in fact) a definition for datum planes has been sought by ASME and ISO standards writers that combines the contacting nature of traditional surface plate mating with a means of balancing rocking conditions when there is a centrally positioned extreme point or edge on the datum feature. This paper describes a completely self-balancing method for datum plane establishment that matches traditional surface plate mating while automatically stabilizing rocker conditions. The method is based on a constrained L2 (L2) minimization, which, when seen mathematically, elegantly combines the desirable contact properties of the constrained L1 (L1) minimization with the stable properties of the unconstrained least-squares and does so in a manner that avoids the drawbacks of either of those two definitions. The definition is shown along with proofs of a mathematical development of an algorithm that relies on a strategically chosen singular value decomposition that allows for an elegant, robust solution. Concise code is included for the reader for actual use as well as to full clarify all the algorithmic details.Testing has shown the definition defined here does indeed provide attractive balancing of full contact with rocker stability, leading to guarded optimism on the part of the key standards committees as an attractive default definition. Since both the ISO and ASME standardization efforts are actively working to establish default datum plane definitions, the timing of such a rigorously documented study is opportune.

Fitting Weighted Total Least-Squares Planes and Parallel Planes to Support Tolerancing Standards

We present elegant algorithms for fitting a plane, two parallel planes (corresponding to a slot or a slab) or many parallel planes in a total (orthogonal) least-squares sense to coordinate data that is weighted. Each of these problems is reduced to a simple 3×3 matrix eigenvalue/eigenvector problem or an equivalent singular value decomposition problem, which can be solved using reliable and readily available commercial software. These methods were numerically verified by comparing them with brute-force minimization searches. We demonstrate the need for such weighted total least-squares fitting in coordinate metrology to support new and emerging tolerancing standards, for instance, ISO 14405-1:2010. The widespread practice of unweighted fitting works well enough when point sampling is controlled and can be made uniform (e.g., using a discrete point contact Coordinate Measuring Machine). However, we demonstrate that nonuniformly sampled points (arising from many new measurement technologies) coupled with unweighted least-squares fitting can lead to erroneous results. When needed, the algorithms presented also solve the unweighted cases simply by assigning the value one to each weight. We additionally prove convergence from the discrete to continuous cases of least-squares fitting as the point sampling becomes dense.

Performing three-dimensional measurements on micro-scale features using a flexible coordinate measuring machine fiber probe with ellipsoidal tip

The tip of a traditional coordinate measuring machine (CMM) probe used for measurements of macro-scale artifacts is generally a sphere of excellent geometry. Its known diameter (from a prior calibration) and form, along with the known approach direction (which is normal to the surface), facilitate probe radius compensation in a straightforward manner. Neither of these conditions is valid for micro-scale measurements made with a flexible fiber probe on a CMM. This presents two challenges. The first involves the calibration of the probes true size and shape. The second involves developing a method for compensating probe radius and form on measurement data from test artifacts. We describe these issues here in the context of an application involving three-dimensional measurements on micro-scale features (a conical section of 20° half angle and a rounded tip of 38 µm radius) performed with the NIST fiber probe (Muralikrishnan et al 2006 Precis. Eng. 30 154–64).

An improved L1 based algorithm for standardized planar datum establishment

This paper has two major goals. First, we present an algorithm for establishing planar datums suitable for a default in tolerancing standards. The algorithm is based on a constrained minimization search based on the L1 (L1) norm after forming a convex surface from the original surface or sampled points. We prove that the problem reduces to a simple minimization search between the convex surface and its centroid. The data points in the discrete case do not need to have any corresponding weights provided with them, as appropriate weighting is part of the algorithm itself, thereby making the algorithm largely insensitive to nonuniformly sampled data points. Terse Mathematica code is included for the reader. The code is sufficient for constrained and unconstrained planar fitting as well as a 3-2-1 datum reference frame generation. The second goal of this paper is to compare this new method with several other possible means for establishing datum planes, ultimately showing several appealing characteristics of the proposed algorithm. Since both the ISO and ASME standardization efforts are actively working to establish datum plane definitions, the timing of such a study is opportune.© 2014 ASME