Toward Guaranteed Illumination Models for Non-Convex Objects

Illumination variation remains a central challenge in object detection and recognition. Existing analyses of illumination variation typically pertain to convex, Lambertian objects, and guarantee quality of approximation in an average case sense. We show that it is possible to build V(vertex)-description convex cone models with worst-case performance guarantees, for non-convex Lambertian objects. Namely, a natural verification test based on the angle to the constructed cone guarantees to accept any image which is sufficiently well-approximated by an image of the object under some admissible lighting condition, and guarantees to reject any image that does not have a sufficiently good approximation. The cone models are generated by sampling point illuminations with sufficient density, which follows from a new perturbation bound for point images in the Lambertian model. As the number of point images required for guaranteed verification may be large, we introduce a new formulation for cone preserving dimensionality reduction, which leverages tools from sparse and low-rank decomposition to reduce the complexity, while controlling the approximation error with respect to the original cone

Evaluating Outer Segment Length as A Surrogate Measure of Peak Foveal Cone Density

Adaptive optics (AO) imaging tools enable direct visualization of the cone photoreceptor mosaic, which facilitates quantitative measurements such as cone density. However, in many individuals, low image quality or excessive eye movements precludes making such measures. As foveal cone specialization is associated with both increased density and outer segment (OS) elongation, we sought to examine whether OS length could be used as a surrogate measure of foveal cone density. The retinas of 43 subjects (23 normal and 20 albinism; aged 6–67 years) were examined. Peak foveal cone density was measured using confocal adaptive optics scanning light ophthalmoscopy (AOSLO), and OS length was measured using optical coherence tomography (OCT) and longitudinal reflectivity profile-based approach. Peak cone density ranged from 29,200 to 214,000 cones/mm2(111,700 ± 46,300 cones/mm2); OS length ranged from 26.3 to 54.5 μm (40.5 ± 7.7 μm). Density was significantly correlated with OS length in albinism (p \u3c 0.0001), but not normals (p = 0.99). A cubic model of density as a function of OS length was created based on histology and optimized to fit the albinism data. The model includes triangular cone packing, a cylindrical OS with a fixed volume of 136.6 μm3, and a ratio of OS to inner segment width that increased linearly with increasing OS length (R2 = 0.72). Normal subjects showed no apparent relationship between cone density and OS length. In the absence of adequate AOSLO imagery, OS length may be used to estimate cone density in patients with albinism. Whether this relationship exists in other patient populations with foveal hypoplasia (e.g., premature birth, aniridia, isolated foveal hypoplasia) remains to be seen

Repeatability of \u3cem\u3eIn Vivo\u3c/em\u3e Parafoveal Cone Density and Spacing Measurements

Purpose. To assess the repeatability and measurement error associated with cone density and nearest neighbor distance (NND) estimates in images of the parafoveal cone mosaic obtained with an adaptive optics scanning light ophthalmoscope (AOSLO).Methods. Twenty-one participants with no known ocular pathology were recruited. Four retinal locations, approximately 0.65[degrees] eccentricity from the center of fixation, were imaged 10 times in randomized order with an AOSLO. Cone coordinates in each image were identified using an automated algorithm (with or without manual correction) from which cone density and NND were calculated. Owing to naturally occurring fixational instability, the 10 images recorded from a given location did not overlap entirely. We thus analyzed each image set both before and after alignment.Results. Automated estimates of cone density on the unaligned image sets showed a coefficient of repeatability of 11,769 cones/mm2 (17.1%). The primary reason for this variability appears to be fixational instability, as aligning the 10 images to include the exact same retinal area results in an improved repeatability of 4358 cones/mm2 (6.4%) using completely automated cone identification software. Repeatability improved further by manually identifying cones missed by the automated algorithm, with a coefficient of repeatability of 1967 cones/mm2 (2.7%). NND showed improved repeatability and was generally insensitive to the undersampling by the automated algorithm.Conclusions. As our data were collected in a young, healthy population, this likely represents a best-case estimate for corresponding measurements in patients with retinal disease. Similar studies need to be carried out on other imaging systems (including those using different imaging modalities, wavefront correction technology, and/or image analysis software), as repeatability would be expected to be highly sensitive to initial image quality and the performance of cone identification algorithms. Separate studies addressing intersession repeatability and interobserver reliability are also needed

Functional evidence for cone-specific connectivity in the human retina

NoPhysiological studies of colour vision have not yet resolved the controversial issue of how chromatic opponency is constructed at a neuronal level. Two competing theories, the cone-selective hypothesis and the random-wiring hypothesis, are currently equivocal to the architecture of the primate retina. In central vision, both schemes are capable of producing colour opponency due to the fact that receptive field centres receive input from a single bipolar cell ¿ the so called `private line arrangement¿. However, in peripheral vision this single-cone input to the receptive field centre is lost, so that any random cone connectivity would result in a predictable reduction in the quality of colour vision. Behavioural studies thus far have indeed suggested a selective loss of chromatic sensitivity in peripheral vision. We investigated chromatic sensitivity as a function of eccentricity for the cardinal chromatic (L/M and S/(L + M)) and achromatic (L + M) pathways, adopting stimulus size as the critical variable. Results show that performance can be equated across the visual field simply by a change of scale (size). In other words, there exists no qualitative loss of chromatic sensitivity across the visual field. Critically, however, the quantitative nature of size dependency for each of the cardinal chromatic and achromatic mechanisms is very specific, reinforcing their independence in terms of anatomy and genetics. Our data provide clear evidence for a physiological model of primate colour vision that retains chromatic quality in peripheral vision, thus supporting the cone-selective hypothesis

Block Factor-width-two Matrices and Their Applications to Semidefinite and Sum-of-squares Optimization

Semidefinite and sum-of-squares (SOS) optimization are fundamental computational tools in many areas, including linear and nonlinear systems theory. However, the scale of problems that can be addressed reliably and efficiently is still limited. In this paper, we introduce a new notion of \emph{block factor-width-two matrices} and build a new hierarchy of inner and outer approximations of the cone of positive semidefinite (PSD) matrices. This notion is a block extension of the standard factor-width-two matrices, and allows for an improved inner-approximation of the PSD cone. In the context of SOS optimization, this leads to a block extension of the \emph{scaled diagonally dominant sum-of-squares (SDSOS)} polynomials. By varying a matrix partition, the notion of block factor-width-two matrices can balance a trade-off between the computation scalability and solution quality for solving semidefinite and SOS optimization. Numerical experiments on large-scale instances confirm our theoretical findings.Comment: 26 pages, 5 figures. Added a new section on the approximation quality analysis using block factor-width-two matrices. Code is available through https://github.com/zhengy09/SDPf