Portable 3D laser-camera calibration system with color fusion for SLAM

Nowadays, the use of RGB-D sensors have focused a lot of research in computer vision and robotics. These kinds of sensors, like Kinect, allow to obtain 3D data together with color information. However, their working range is limited to less than 10 meters, making them useless in some robotics applications, like outdoor mapping. In these environments, 3D lasers, working in ranges of 20-80 meters, are better. But 3D lasers do not usually provide color information. A simple 2D camera can be used to provide color information to the point cloud, but a calibration process between camera and laser must be done. In this paper we present a portable calibration system to calibrate any traditional camera with a 3D laser in order to assign color information to the 3D points obtained. Thus, we can use laser precision and simultaneously make use of color information. Unlike other techniques that make use of a three-dimensional body of known dimensions in the calibration process, this system is highly portable because it makes use of small catadioptrics that can be placed in a simple manner in the environment. We use our calibration system in a 3D mapping system, including Simultaneous Location and Mapping (SLAM), in order to get a 3D colored map which can be used in different tasks. We show that an additional problem arises: 2D cameras information is different when lighting conditions change. So when we merge 3D point clouds from two different views, several points in a given neighborhood could have different color information. A new method for color fusion is presented, obtaining correct colored maps. The system will be tested by applying it to 3D reconstruction.

Portable 3D laser-camera calibration system with color fusion for SLAM

Paper submitted to the 43rd International Symposium on Robotics (ISR2012), Taipei, Taiwan, Aug. 29-31, 2012.

Primary school teacher’s noticing of students’ mathematical thinking in problem solving

Professional noticing of students’ mathematical thinking in problem solving involves the identification of noteworthy mathematical ideas of students’ mathematical thinking and its interpretation to make decisions in the teaching of mathematics. The goal of this study is to begin to characterize pre-service primary school teachers’ noticing of students’ mathematical thinking when students solve tasks that involve proportional and non-proportional reasoning. From the analysis of how pre-service primary school teachers notice students’ mathematical thinking, we have identified an initial framework with four levels of development. This framework indicates a possible trajectory in the development of primary teachers’ professional noticing.