Variational Uncalibrated Photometric Stereo under General Lighting

Photometric stereo (PS) techniques nowadays remain constrained to an ideal laboratory setup where modeling and calibration of lighting is amenable. To eliminate such restrictions, we propose an efficient principled variational approach to uncalibrated PS under general illumination. To this end, the Lambertian reflectance model is approximated through a spherical harmonic expansion, which preserves the spatial invariance of the lighting. The joint recovery of shape, reflectance and illumination is then formulated as a single variational problem. There the shape estimation is carried out directly in terms of the underlying perspective depth map, thus implicitly ensuring integrability and bypassing the need for a subsequent normal integration. To tackle the resulting nonconvex problem numerically, we undertake a two-phase procedure to initialize a balloon-like perspective depth map, followed by a "lagged" block coordinate descent scheme. The experiments validate efficiency and robustness of this approach. Across a variety of evaluations, we are able to reduce the mean angular error consistently by a factor of 2-3 compared to the state-of-the-art.Comment: Haefner and Ye contributed equall

Direct frequency comb measurements of absolute optical frequencies and population transfer dynamics

A phase-stabilized femtosecond laser comb is directly used for high-resolution spectroscopy and absolute optical frequency measurements of one- and two-photon transitions in laser-cooled \rb atoms. Absolute atomic transition frequencies, such as the 5S$_{1/2}$ F=2 \ra 7S$_{1/2}$ F"=2 two-photon resonance measured at 788 794 768 921(44) kHz, are determined without \textit{a priori} knowledge about their values. Detailed dynamics of population transfer driven by a sequence of pulses are uncovered and taken into account for the measurement of the 5P states via resonantly enhanced two-photon transitions.Comment: 5 pages, 4 figures, submitte

The Impact of Inappropriate Modeling of Cross-Classified Data Structures on Random-Slope Models

Previous studies that explored the impact of misspecification of cross-classified data structure as strictly hierarchical are limited to random intercept models. This study examined the effects of misspecification of a two-level, cross-classified, random effect model (CCREM) where both the level-1 intercept and slope were allowed to vary randomly. Results suggest that ignoring one of the crossed factors produced considerably underestimated standard errors for: 1) the regression coefficients of the level-1 predictor; 2) the inappropriately modeled predictor associated with the misspecified crossed factor; and 3) and their interaction. This misspecification also resulted in a significant inflation of the level-1 residual variances and the intercept and slope variance components across the levels of the remaining crossed factor in hierarchical linear model

Paleogeographic, Paleoceanographic, and Tectonic Controls on Early Late Ordovician Graptolite Diversity Patterns

The Katian Age (early Late Ordovician) was a time of significant decline in marine biodiversity, but whether this decline was a real phenomenon or an artifact of the relatively few studies devoted to this interval requires further research. We examined the pattern of graptolite faunal changes across the boundary between the Climacograptus bicornis and Diplacanthograptus caudatus graptolite zones in North America and on several other continents. A sharp decline in species diversity occurs in the Appalachian Basin. Scores for normalized diversity dropped from 20 in the C. bicornis Zone to 7 in the D. caudatus Zone. Only 11% of the species present in the C. bicornis Zone carry over into the D. caudatus Zone. A similar pattern occurs in central Oklahoma. Regions at higher paleolatitude, such as Wales and Baltoscandia, exhibit low graptolite diversity in lower Katian strata, and then diversity declines further in higher strata. In other regions at low paleolatitude, such as Australasia and Scotland, however, diversity is fairly constant across this interval (although the percentage of carryover taxa remains low). We conclude that seawater temperature change or disruption of the oceanic density structure, which might accompany temperature change, provides explanations for the similarity between Laurentian and higher paleolatitude diversity patterns. Flooding of the Laurentian craton through the Sebree Trough by cool, subpolar Iapetus seawater may have adversely affected graptolite diversity there. Regions at high paleolatitudes likely underwent cooling associated with Katian climate deterioration. Thus seawater cooling, albeit driven by different mechanisms, may have produced similar diversity patterns at different paleolatitudes