In this paper, the numerical error of two widely used methods for remapping of discrete quantities from one computational mesh to another is investigated. We compare the intuitive, but resource intensive method utilizing intersections of computational cells with the faster and simpler swept-region-based method. Both algorithms are formally second order accurate, however, they are known to produce slightly different quantity profiles in practical applications. The second-order estimate of the error formula is constructed algebraically for both algorithms so that their local accuracy can be evaluated. This general estimate is then used to assess the dependence of the performance of both methods on parameters such as the second derivatives of the remapped distribution, mesh geometry or mesh movement. Due to the complexity of such analysis, it is performed on a set of simplified elementary mesh patterns such as cell corner expansion, rotation or shear. On selected numerical tests it is demonstrated that the swept-based method can distort a symmetric quantity distribution more substantially than the intersection-based approach when the computational mesh moves in an unsuitable direction.

A basic principle in visual neuroscience is the retinotopic organization of neural receptive fields. Here, we review behavioral, neurophysiological, and neuroimaging evidence for nonretinotopic processing of visual stimuli. A number of behavioral studies have shown perception depending on object or external-space coordinate systems, in addition to retinal coordinates. Both single-cell neurophysiology and neuroimaging have provided evidence for the modulation of neural firing by gaze position and processing of visual information based on craniotopic or spatiotopic coordinates. Transient remapping of the spatial and temporal properties of neurons contingent on saccadic eye movements has been demonstrated in visual cortex, as well as frontal and parietal areas involved in saliency/priority maps, and is a good candidate to mediate some of the spatial invariance demonstrated by perception. Recent studies suggest that spatiotopic selectivity depends on a low spatial resolution system of maps that operates over a longer time frame than retinotopic processing and is strongly modulated by high-level cognitive factors such as attention. The interaction of an initial and rapid retinotopic processing stage, tied to new fixations, and a longer lasting but less precise nonretinotopic level of visual representation could underlie the perception of both a detailed and a stable visual world across saccadic eye movements.

Even during active fixation, small eye movements persist that might be expected to interfere with vision. Numerous brain mechanisms probably contribute to discounting this jitter. Changes in the timing of responses in the visual thalamus associated with fixational saccades are considered in this study. Activity of single neurons in alert monkey lateral geniculate nucleus (LGN) was recorded during fixation while pseudorandom visual noise stimuli were presented. The position of the stimulus on the display monitor was adjusted based on eye position measurements to control for changes in retinal locations due to eye movements. A method for extracting nonstationary first-order response mechanisms was applied, so that changes around the times of saccades could be observed. Saccade-related changes were seen in both amplitude and timing of geniculate responses. Amplitudes were greatly reduced around saccades. Timing was retarded slightly during a window of about 200 ms around saccades. That is, responses became more sustained. These effects were found in both parvocellular and magnocellular neurons. Timing changes in LGN might play a role in maintaining cortical responses to visual stimuli in the presence of eye movements, compensating for the spatial shifts caused by saccades via these shifts in timing.