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This paper describes algorithms for generating 3-D point clouds from a set of digital images obtained from projecting phase-shifted sinusoidal fringe patterns onto object. In this paper, a mathematical model is introduced for describing the geometric relationship between the fringe patterns being projected, the image captured and the shape of the object being measured. This model allows considerable flexibility in the spatial configuration of shape measurement system. The algorithms for point cloud construction described in this paper present an improvement over the existing algorithms in terms of accuracy, ease of system calibration, and sensitivity to parameter errors. These algorithms have been incorporated in a shape measurement system and shown to have a very good performance.Keywords: 3-D shape measurement, fringe projection, point cloud generation, triangulation. INTRODUCTIONMany industrial applications require accurate and rapid measurement of the 3-D shapes of objects. Representative applications of 3-D shape measurement include reverse engineering, 3D replication, inspection and quality control. In most of these applications, users need to construct 3D point clouds that correspond to the objects surface by performing measurement on the objects surfaces. Manufacturing industry needs a fast inspection process that can measure and analyze various 3D features on the part and determine if a feature is within the tolerance specifications or not. The measurement scheme needs to be adequately accurate to eliminate measurement errors. Measurement errors can lead to erroneous inspection that results in an acceptable part being rejected and a defective part being accepted. Hence, both inspection speed and accuracy are equally important. Coordinate measurement machines and laser based measurement techniques usually provide very accurate measurements. However, these techniques are slow because they measure various points on the part sequentially. On the other hand, camera-based techniques are usually very fast. Therefore, a possible way to perform the 3D inspection is to use digital cameras to construct a dense point cloud (e.g., points spaced less then 0.25mm apart) corresponding to the part being inspected and then analyze the point cloud to determine if it meets the tolerance specifications. But accuracy associated with the conventional camera-based inspection techniques has not been very high in the area of measurement of geometrically complex 3D shapes. Shape measurement based on digital fringe projection (SMDFP) is a technique for non-contact shape measurement. Due to its fast speed, flexibility, low cost and potentially high accuracy, SMDFP has shown great promise in 3-D shape measurement, especially for applications that require acquisition of dense point clouds. A typical SMDFP system contains one projection unit and one or more cameras (a schematic of a SMDFP system with one projector and one camera is shown in Fig. 1). During the shape measurement process, a set of fringe patterns, whose structur...

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