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Estimation of 3-D information from 2-D image coordinates is a fundamental problem both in machine vision and computer vision. Circular features are the most common quadratic-curved features that have been addressed for 3-D location estimation. In this paper, a closed-form analytical solution to the problem of 3-D location estimation of circular features is presented. Two different cases are considered: 1) 3-D orientation and 3-D position estimation of a circular feature when its radius is known, and 2) 3-D orientation and 3-D position estimation of a circular feature when its radius is not known. As well, extension of the developed method to 3-D quadratic features is addressed. Specifically, a closed-form analytical solution is derived for 3-D position estimation of spherical features. For experimentation purposes, simulated as well as real setups were employed. Simulated experimental results obtained for all three cases mentioned above verified the analytical method developed in this paper. In the case of real experiments, a set of circles located on a calibration plate, whose locations were known with respect to a reference frame, were used for camera calibration as well as for the application of the developed method. Since various distortion factors had to be compensated in order to obtain accurate estimates of the parameters of the imaged circle-an ellipse-with respect to the camera's image frame, a sequential compensation procedure was applied to the input grey-level image. The experimental results obtained once more showed the validity of the total process involved in the 3-D location estimation of circular features in general and the applicability of the analytical method developed in this paper in particular. I. INTRODUCTION STIMATION of 3-D information from 2-D image coor-E dinates is a fundamental problem in both machine vision and computer vision. This problem exists in two forms: the direct and the inverse. When the camera parameters (the intrinsic: effective focal length, lens distortion factors, etc., and the extrinsic: 3-D position and 3-D orientation of the camera frame) are given in addition to the 2-D image coordinates, the problem is of the direct type. On the other hand, if

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A prototype touch-sensitive tablet is presented. The tablet's main innovation is that it is capable of sensing more than one point of contact at a time. In addition to being able to provide position coordinates, the tablet also gives a measure of degree of contact, independently for each point of contact. In order to enable multi-touch sensing, the tablet surface is divided into a grid of discrete points. The points are scanned using a recursive area subdivision algorithm. In order to minimize the resolution lost due to the discrete nature of the grid, a novel interpolation scheme has been developed. Finally, the paper briefly discusses how multi-touch sensing, interpolation, and degree of contact sensing can be combined to expand our vocabulary in human-computer interaction.

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Learning Objectives: On successful completion of this activity, participants should be able to (1) provide an introduction to machine learning, neural networks, and deep learning; (2) discuss common machine learning algorithms with illustrative examples and figures; and (3) compare machine learning algorithms and provide guidance on selection for a given application. Financial Disclosure: Sandra E. Black received in-kind funding to her institution from GE Healthcare and Avid Pharmaceuticals. The authors of this article have indicated no other relevant relationships that could be perceived as a real or apparent conflict of interest. CME Credit: SNMMI is accredited by the Accreditation Council for Continuing Medical Education (ACCME) to sponsor continuing education for physicians. SNMMI designates each JNM continuing education article for a maximum of 2.0 AMA PRA Category 1 Credits. Physicians should claim only credit commensurate with the extent of their participation in the activity. For CE credit, SAM, and other credit types, participants can access this activity through the SNMMI website (http://www.snmmilearningcenter.org) through April 2022. This article, the first in a 2-part series, provides an introduction to machine learning (ML) in a nuclear medicine context. This part addresses the history of ML and describes common algorithms, with illustrations of when they can be helpful in nuclear medicine. Part 2 focuses on current contributions of ML to our field, addresses future expectations and limitations, and provides a critical appraisal of what ML can and cannot do.

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