The Number Line (NL) task requires judging the relative numerical magnitude of a number and estimating its value spatially on a continuous line. Children's skill on this task has been shown to correlate with and predict future mathematical competence. Neurofunctionally, this task has been shown to rely on brain regions involved in numerical processing. However, there is no direct evidence that performance on the NL task is related to brain areas recruited during arithmetical processing and that these areas are domain-specific to numerical processing. In this study, we test whether 8- to 14-year-old's behavioral performance on the NL task is related to fMRI activation during small and large single-digit subtraction problems. Domain-specific areas for numerical processing were independently localized through a numerosity judgment task. Results show a direct relation between NL estimation performance and the amount of the activation in key areas for arithmetical processing. Better NL estimators showed a larger problem size effect than poorer NL estimators in numerical magnitude (i.e., intraparietal sulcus) and visuospatial areas (i.e., posterior superior parietal lobules), marked by less activation for small problems. In addition, the direction of the activation with problem size within the IPS was associated to differences in accuracies for small subtraction problems. This study is the first to show that performance in the NL task, i.e. estimating the spatial position of a number on an interval, correlates with brain activity observed during single-digit subtraction problem in regions thought to be involved numerical magnitude and spatial processes.
A novel method of estimating the viewing position of a single perspective projection image is presented in this paper. This method is based on a set of newly defined Fourier descriptors (FDs) to describe the contour of a planar shape lies in the three dimensional (3-D) domain. In order to generate the 3-D planar image from the 2-D perspective image, we use the inverse paraperspective transformation instead of the inverse perspective transformation. Based on the linear feature of the paraperspective transformation, some new FDs for the 3-D planar contour have been developed. They are proved to be solely dependent on the FDs of the contour of the 2-D projected image and the slope of the world plane. Thereatter, ways for simple and efficient estimation of the unknown viewing position can be achieved.
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