@article{lee_krim_2017, title={Sampling Density Criterion for Circular Structured Light 3D Imaging}, DOI={10.5220/0006147504780483}, abstractNote={3D reconstruction work has chiefly focused on the accuracy of reconstruction results in computer vision, and efficient 3D functional camera system has been of interest in the field of mobile camera as well. The optimal sampling density, referred to as the minimum sampling rate for 3D or high-dimensional signal reconstruction, is proposed in this paper. There have been many research acti vities to develop an adaptive sampling theorem beyond theShannon-Nyquist Sampling Theorem in the areas of signal processing, but sampling theorem for 3D imaging or reconstruction is an open challenging topic an d crucial part of our contribution in this paper. We hence propose an approach to sampling rate (lower / upper b ound) determination to recover 3D objects (surfaces) represented by a set of circular light patterns, a d the criterion for a sampling rate is formulated using geometric characteristics of the light patterns over laid on the surface. The proposed method is in a sense a foundation for a sampling theorem applied to 3D image proce ssing, by establishing a relationship between frequency components and geometric information of a surfac e.}, journal={PROCEEDINGS OF THE 12TH INTERNATIONAL JOINT CONFERENCE ON COMPUTER VISION, IMAGING AND COMPUTER GRAPHICS THEORY AND APPLICATIONS (VISIGRAPP 2017), VOL 6}, author={Lee, Deokwoo and Krim, Hamid}, year={2017}, pages={478–483} }
 @inproceedings{lee_krim_2012, title={A sampling theorem for a 2D surface}, volume={6667}, DOI={10.1007/978-3-642-24785-9_47}, abstractNote={The sampling rate for signal reconstruction has been and remains an important and central criterion in numerous applications. We propose, in this paper, a new approach to determining an optimal sampling rate for a 2D-surface reconstruction using the so-called Two-Thirds Power Law. This paper first introduces an algorithm of a 2D surface reconstruction from a 2D image of circular light patterns projected on the surface. Upon defining the Two-Thirds Power Law we show how the extracted spectral information helps define an optimal sampling rate of the surface, reflected in the number of projected circular patterns required for its reconstruction. This result is of interest in a number of applications such as 3D face recognition and development of new efficient 3D cameras. Substantive examples are provided.}, booktitle={Scale space and variational methods in computer vision}, author={Lee, D. and Krim, H.}, year={2012}, pages={556–567} }
 @inproceedings{lee_krim_2010, title={3D surface reconstruction using structured circular light patterns}, volume={6474}, DOI={10.1007/978-3-642-17688-3_27}, abstractNote={Reconstructing a 3D surface in ℝ3 from a 2D image in ℝ2 has been a widely studied issue as well as one of the most important problems in image processing. In this paper, we propose a novel approach to reconstructing 3D coordinates of a surface from a 2D image taken by a camera using projected circular light patterns. Known information (i.e. intrinsic and extrinsic parameters of the camera, the structure of the circular patterns, a fixed optical center of the camera and the location of the reference plane of the surface) provides a mathematical model for surface reconstruction. The reconstruction is based on a geometrical relationship between a given pattern projected onto a 3D surface and a pattern captured in a 2D image plane from a viewpoint. This paper chiefly deals with a mathematical proof of concept for the reconstruction problem.}, booktitle={Advanced concepts for intelligent vision systems, pt i}, author={Lee, D. and Krim, H.}, year={2010}, pages={279–289} }