Physically Consistent Preferential Bayesian Optimization for Food Arrangement

This paper considers the problem of estimating a preferred food arrangement for users from interactive pairwise comparisons using Computer Graphics (CG)-based dish images. As a foodservice industry requirement, we need to utilize domain rules for the geometry of the arrangement (e.g., the food layout of some Japanese dishes is reminiscent of mountains). However, those rules are qualitative and ambiguous; the estimated result might be physically inconsistent (e.g., each food physically interferes, and the arrangement becomes infeasible). To cope with this problem, we propose Physically Consistent Preferential Bayesian Optimization (PCPBO) as a method that obtains physically feasible and preferred arrangements that satisfy domain rules. PCPBO employs a bi-level optimization that combines a physical simulation-based optimization and a Preference-based Bayesian Optimization (PbBO). Our experimental results demonstrated the effectiveness of PCPBO on simulated and actual human users.Comment: 8 pages, 10 figures, accepted by IEEE Robotics and Automation Letters (RA-L) 202

Multivariable Logistic Regression Model: A Novel Mathematical Model that Predicts Visual Field Sensitivity from Macular Ganglion Cell Complex Thickness in Glaucoma

<div><p>Purpose</p><p>To design a mathematical model that can predict the relationship between the ganglion cell complex (GCC) thickness and visual field sensitivity (VFS) in glaucoma patients.</p><p>Design</p><p>Retrospective cross-sectional case series.</p><p>Method</p><p>Within 3 months from VFS measurements by the Humphrey field analyzer 10-2 program, 83 eyes underwent macular GCC thickness measurements by spectral-domain optical coherence tomography (SD-OCT). Data were used to construct a multiple logistic model that depicted the relationship between the explanatory variables (GCC thickness, age, sex, and spherical equivalent of refractive errors) determined by a regression analysis and the mean VFS corresponding to the SD-OCT scanned area. Analyses were performed in half or 8 segmented local areas as well as in whole scanned areas. A simple logistic model that included GCC thickness as the single explanatory variable was also constructed. The ability of the logistic models to depict the real GCC thickness/VFS in SAP distribution was analyzed by the χ² test of goodness-of-fit. The significance of the model effect was analyzed by analysis of variance (ANOVA).</p><p>Results</p><p>Scatter plots between the GCC thickness and the mean VFS showed sigmoid curves. The χ² test of goodness-of-fit revealed that the multiple logistic models showed a good fit for the real GCC thickness/VFS distribution in all areas except the nasal-inferior-outer area. ANOVA revealed that all of the multiple logistic models significantly predicted the VFS based on the explanatory variables. Although simple logistic models also exhibited significant VFS predictability based on the GCC thickness, the model effect was less than that observed for the multiple logistic models.</p><p>Conclusions</p><p>The currently proposed logistic models are useful methods for depicting relationships between the explanatory variables, including the GCC thickness, and the mean VFS in glaucoma patients.</p></div

Comparison of R² values between presented models and previous models.

<p>GCA = ganglion cell layer and inner plexiform layer.</p><p>* R² values between ganglion cell complex thickness and mean deviation value of 24-2.</p>†<p>R² values between GCA thickness and mean visual filed sensitivity by microperimetry.</p

The outcome of the χ² test of goodness-of-fit, ANOVA, and the R² of the multiple logistic models.

<p>The outcome of the χ² test of goodness-of-fit, ANOVA, and the R² of the multiple logistic models.</p

Methods of analysis for the macular ganglion cell complex thickness and standard automated perimetry.

<p><b>A</b>) Representative ganglion cell complex (GCC) thickness map analyzed by RS-3000. Dividing lines and circles were drawn by the build-in software. <b>B</b>) Grayscale of the Humphrey visual field analyzer central 10-2 program in the same patient. <b>C</b>) Adjustment of the standard automated perimetry (SAP) test points to the GCC-map divided areas (GMDAs). Each inner GMDA (3-1 to 3-4) included three SAP test points (asterisks). Each asterisk of the SAP test points corresponds to the same color asterisk in the GCC map (top left). Each outer GMDA (6-1 to 6-4) includes 14 SAP test points. Note that the # is adjusted to the outer GMDA. <b>D</b>) Measurement of the GCC thickness in the superior and inferior areas. Numerical values in each area represent the mean GCC thickness (µm) of the area. <b>E</b>) Measurement of the GCC thickness in eight divided areas. These areas were named <i>3-1</i> to <i>6-4</i> GMDAs. Numerical values in each area represent the mean GCC thickness (µm) of the area. <b>F</b>) Mean visual field sensitivity is indicated in each GMDA.</p

The outcome of the χ² test of goodness-of-fit, ANOVA, and the R² of the simple logistic models.

<p>The outcome of the χ² test of goodness-of-fit, ANOVA, and the R² of the simple logistic models.</p

The estimated parameters of the explanatory variables obtained from the simple logistic regression analysis.

<p>The estimated parameters of the explanatory variables obtained from the simple logistic regression analysis.</p

The estimated parameters and <i>p</i>-values of the explanatory variables obtained from the multiple logistic regression analysis.

<p>The estimated parameters and <i>p</i>-values of the explanatory variables obtained from the multiple logistic regression analysis.</p