During the creative process, designers use various techniques and strategies to move from the abstract to the concrete, utilizing different physical and virtual means to represent form. The changes between virtual and physical models are not always fluent, however. Differential 3D scanning can detect the differences between a scanned model (point cloud) and a reference model (polygon mesh or CAD model) and then reflect those changes in the reference model. This can save designers time by reconstructing only the small changed regions rather than the entire object.

In this paper, we present a novel computational puzzle solver for square-piece image jigsaw puzzles with no prior information such as piece orientation, anchor pieces or resulting dimension of the puzzle. By "piece" we mean a square dxd block of pixels, where we investigate pieces as small as 7x7 pixels. To reconstruct such challenging puzzles, we aim to search for piece configurations which maximize the size of consensus (i.e. grid or loop) configurations which represent a geometric consensus or agreement among pieces. Pieces are considered for addition to the existing assemblies if these pieces increase the size of the consensus configurations. In contrast to previous puzzle solvers which goal for assemblies maximizing compatibility measures between all pairs of pieces and thus depend heavily on the pairwise compatibility measure used, our new approach reduces the dependency on the pairwise compatibility measures which become increasingly uninformative at small scales and instead exploits geometric agreement among pieces. Our contribution also includes an improved pairwise compatibility measure which exploits directional derivative information along adjoining boundaries of the pieces. For the challenging unknown orientation piece puzzles where the size of pieces is small, we reduce assembly error by up to 75% compared with previous algorithms for standard datasets.

Human hand motion and shape sensing is an area of high interest in medical communities and for human interaction researchers. Measurement of small hand movements could help professionals to quantize the stage of conditions like Parkinson's Disease (PD) and Essential Tremor (ET). Similar data is also useful for designers of human interaction algorithms to infer information about hand pose and gesture recognition. In this paper we present a structured light sensor capable of measuring hand shape and color at 121 FPS. Our algorithm uses a novel structured light method developed by us, called Chebyshev Phase Shifting (CPS). This method uses a digital projector and a camera to create high-resolution color 3D models from sequences of color images. We show how to encode CPS patterns in three RGB images for a reduced acquisition time, enabling high speed capture. We have built a prototype to measure rapid trembling hands. Our results show our prototype accurately captures fast tremors similar to those of PD patients. Color 3D model sequences recorded at high speed with our sensor will be used to study hand kinematic properties in a future.

Figure 4 5 6 7 and 8 show qualitative reconstruction results on the challenging unknown orientation piece puzzles from MIT dataset [1]. We varied the number of pieces and the size of each piece for the experiments. When the size of the piece is small, previous algorithms [2, 3] drastically drop their reconstruction performance whereas our proposed algorithm keeps the performance. Our proposed algorithm reduces up to 75% error from the previous work [3] on the unknown orientation piece puzzles (P=14, K=1064).

We introduce Embedded PS, a new robust and accurate phase shifting algorithm for 3D scanning. The method projects only high frequency sinusoidal patterns in order to reduce errors due to global illumination effects, such as subsurface scattering and interreflections. The frequency set for the projected patterns is specially designed so that our algorithm can extract a set of embedded low frequency sinusoidals with simple math. All the signals, patterns high and embedded low frequencies, are used with temporal phase unwrapping to compute absolute phase values in closed-form, without quantization or approximation via LUT, resulting in fast computation. The absolute phases provide correspondences from projector to camera pixels which enable to recover 3D points using optical triangulation. The algorithm estimates multiple absolute phase values per pixel which are combined to reduce measurement noise while preserving fine details. We prove that embedded periodic signals can be recovered from any periodic signal, not just sinusoidal signals, which may result in further improvements for other 3D imaging methods. Several experiments are presented showing that our algorithm produces more robust and accurate 3D scanning results than state-of-the-art methods for challenging surface materials, with an equal or smaller number of projected patterns and at lower computational cost.

Various Structured Light (SL) methods are used to capture 3D range images, where a number of binary or continuous light patterns are sequentially projected onto a scene of interest, while a digital camera captures images of the illuminated scene. All existing SL methods require the projector and camera to be hardware or software synchronized, with one image captured per projected pattern. A 3D range image is computed from the captured images. The two synchronization methods have disadvantages, which limit the use of SL methods to niche industrial and low quality consumer applications. Unsynchronized Structured Light (USL) is a novel SL method which does not require synchronization of pattern projection and image capture. The light patterns are projected and the images are captured independently, at constant, but possibly different, frame rates. USL synthesizes new binary images as would be decoded from the images captured by a camera synchronized to the projector, reducing the subsequent computation to standard SL. USL works both with global and rolling shutter cameras. USL enables most burst-mode-capable cameras, such as modern smartphones, tablets, DSLRs, and point-and-shoots, to function as high quality 3D snapshot cameras. Beyond the software, which can run in the devices, a separate SL Flash, able to project the sequence of patterns cyclically, during the acquisition time, is needed to enable the functionality.

3D Printing has entered the mainstream. Multiple low cost desktop 3D printers are currently available from various vendors, and open source projects let hobbyists build their own. This course addresses the problem of creating 3D models for 3D printing. As is the case for 3D printers, low-cost homemade 3D scanners are now within reach of students and hobbyists with a modest budget. This course provides the students with the necessary mathematics, software, and practical details to leverage projector-camera systems to build their own desktop 3D scanner. An example-driven approach is used throughout, with each new concept illustrated using a practical scanner implemented with off-the-shelf parts. First, the mathematics of triangulation is explained using the intersection of parametric and implicit representations of lines and planes in 3D. The particular case of ray-plane triangulation is illustrated using a scanner built with a single camera and a modified laser pointer. Camera calibration is explained at this stage to convert image measurements to geometric quantities. The mathematics of rigid-body transformations are covered through this example. Next, the details of projector calibration are explained through the development of a classic structured light scanning system using a single camera and projector pair. A minimal postprocessing pipeline is described to convert the point-based representations produced by these scanners to watertight meshes. Key topics covered in this section include: surface representations, file formats, data structures, polygonal meshes, and basic smoothing and gap-filling operations. The course concludes with the description of some commercially available low cost desktop 3D scanners.

Structured-light systems are simple and effective tools to acquire 3D models. Built with off-the-shelf components, a data projector and a camera, they are easy to deploy and compare in precision with expensive laser scanners. But such a high precision is only possible if camera and projector are both accurately calibrated. Robust calibration methods are well established for cameras but, while cameras and projectors can both be described with the same mathematical model, it is not clear how to adapt these methods to projectors. In consequence, many of the proposed projector calibration techniques make use of a simplified model, neglecting lens distortion, resulting in loss of precision. In this paper, we present a novel method to estimate the image coordinates of 3D points in the projector image plane. The method relies on an uncalibrated camera and makes use of local homographies to reach sub-pixel precision. As a result, any camera model can be used to describe the projector, including the extended pinhole model with radial and tangential distortion coefficients, or even those with more complex lens distortion models.