1. Using the two-dimensional (2D) spatial and spectral response profiles described in the previous two reports, we test Daugman's generalization of Marcelja's hypothesis that simple receptive fields belong to a class of linear spatial filters analogous to those described by Gabor and referred to here as 2D Gabor filters. 2. In the space domain, we found 2D Gabor filters that fit the 2D spatial response profile of each simple cell in the least-squared error sense (with a simplex algorithm), and we show that the residual error is devoid of spatial structure and statistically indistinguishable from random error. 3. Although a rigorous statistical approach was not possible with our spectral data, we also found a Gabor function that fit the 2D spectral response profile of each simple cell and observed that the residual errors are everywhere small and unstructured. 4. As an assay of spatial linearity in two dimensions, on which the applicability of Gabor theory is dependent, we compare the filter parameters estimated from the independent 2D spatial and spectral measurements described above. Estimates of most parameters from the two domains are highly correlated, indicating that assumptions about spatial linearity are valid. 5. Finally, we show that the functional form of the 2D Gabor filter provides a concise mathematical expression, which incorporates the important spatial characteristics of simple receptive fields demonstrated in the previous two reports. Prominent here are 1) Cartesian separable spatial response profiles, 2) spatial receptive fields with staggered subregion placement, 3) Cartesian separable spectral response profiles, 4) spectral response profiles with axes of symmetry not including the origin, and 5) the uniform distribution of spatial phase angles. 6. We conclude that the Gabor function provides a useful and reasonably accurate description of most spatial aspects of simple receptive fields. Thus it seems that an optimal strategy has evolved for sampling images simultaneously in the 2D spatial and spatial frequency domains.

1. A reverse correlation (6, 8, 25, 35) method is developed that allows quantitative determination of visual receptive-field structure in two spatial dimensions. This method is applied to simple cells in the cat striate cortex. 2. It is demonstrated that the reverse correlation method yields results with several desirable properties, including convergence and reproducibility independent of modest changes in stimulus parameters. 3. In contrast to results obtained with moving stimuli, we find that the bright and dark excitatory subregions in simple receptive fields do not overlap to any great extent. This difference in results may be attributed to confounding the independent variables space and time when using moving stimuli. 4. All simple receptive fields have subregions that vary smoothly in all directions in space. There are no sharp transitions either between excitatory subregions or between subregions and the area surrounding the receptive field. 5. Simple receptive fields vary both in the number of subregions observed, in the elongation of each subregion, and in the overall elongation of the field. In contrast with results obtained using moving stimuli, we find that subregions within a given receptive field need not be the same length. 6. The hypothesis that simple receptive fields can be modeled as either even symmetric or odd symmetric about a central axis is evaluated. This hypothesis is found to be false in general. Most simple receptive fields are neither even symmetric nor odd symmetric. 7. The hypothesis that simple receptive fields can be modeled as the product of a width response profile and an orthogonal length response profile (Cartesian separability) is evaluated. This hypothesis is found to be true for only approximately 50% of the cells in our sample.

No abstract

PurposeWe investigated the added value of a new respiratory amplitude-based PET reconstruction method called optimal gating (OG) with the aim of providing accurate image quantification in lung cancer.MethodsFDG-PET imaging was performed in 26 lung cancer patients during free breathing using a 24-min list-mode acquisition on a PET/CT scanner. The data were reconstructed using three methods: standard 3D PET, respiratory-correlated 4D PET using a phase-binning algorithm, and OG. These datasets were compared in terms of the maximum SUV (SUVmax) in the primary tumour (main endpoint), noise characteristics, and volumes using thresholded regions of SUV 2.5 and 40% of the SUVmax.ResultsSUVmax values from the 4D method (13.7 ± 5.6) and the OG method (14.1 ± 6.5) were higher (4.9 ± 4.8%, p < 0.001 and 6.9 ± 8.8%, p < 0.001, respectively) than that from the 3D method (13.1 ± 5.4). SUVmax did not differ between the 4D and OG methods (2.0 ± 8.4%, p = NS). Absolute and relative threshold volumes did not differ between methods, except for the 40% SUVmax volume in which the value from the 3D method was lower than that from the 4D method (−5.3 ± 7.1%, p = 0.007). The OG method exhibited less noise than the 4D method. Variations in volumes and SUVmax of up to 40% and 27%, respectively, of the individual gates of the 4D method were also observed.ConclusionThe maximum SUVs from the OG and 4D methods were comparable and significantly higher than that from the 3D method, yet the OG method was visibly less noisy than the 4D method. Based on the better quantification of the maximum and the less noisy appearance, we conclude that OG PET is a better alternative to both 3D PET, which suffers from breathing averaging, and the noisy images of a 4D PET.

No abstract