Development of intra-oral automated landmark recognition (ALR) for dental and occlusal outcome measurements

SummaryPrevious studies embracing digital technology and automated methods of scoring dental arch relationships have shown that such technology is valid and accurate. To date, however there is no published literature on artificial intelligence and machine learning to completely automate the process of dental landmark recognition.This study aimed to develop and evaluate a fully automated system and software tool for the identification of landmarks on human teeth using geometric computing, image segmenting and machine learning technology.239 digital models were used in the automated landmark recognition (ALR) validation phase, 161 of which were digital models from cleft palate subjects aged 5 years. These were manually annotated to facilitate qualitative validation. Additionally, landmarks were placed on 20 adult digital models manually by three independent observers. The same models were subjected to scoring using the ALR software and the differences (in mm) were calculated. All the teeth from the 239 models were evaluated for correct recognition by the ALR with a breakdown to find which stages of the process caused the errors.The results revealed that 1526 out of 1915 teeth (79.7%) were correctly identified, and the accuracy validation gave 95% confidence intervals for the geometric mean error of [0.285, 0.317] for the humans and [0.269, 0.325] for ALR – a negligible difference.It is anticipated that ALR software tool will have applications throughout Dentistry and anthropology and in research will constitute an objective tool for handling large datasets without the need for time intensive employment of experts to place landmarks manually.

ASYMPTOTIC ORDER OF THE GEOMETRIC MEAN ERROR FOR SELF-AFFINE MEASURES ON BEDFORD–MCMULLEN CARPETS

Let [Formula: see text] be a Bedford–McMullen carpet associated with a set of affine mappings [Formula: see text] and let [Formula: see text] be the self-affine measure associated with [Formula: see text] and a probability vector [Formula: see text]. We study the asymptotics of the geometric mean error in the quantization for [Formula: see text]. Let [Formula: see text] be the Hausdorff dimension for [Formula: see text]. Assuming a separation condition for [Formula: see text], we prove that the [Formula: see text]th geometric error for [Formula: see text] is of the same order as [Formula: see text].

Prediction of unsaturated soil hydraulic conductivity using air permeability: Regression approach

A close correlation between water conductivity (<italic>K(θ)</italic>) and air permeability (<italic>K</italic>_{<italic>a</italic>}), measured at various water contents, is expected due to tight dependence of water filled porosity to air filled porosity of soils. Finding such a relation will greatly facilitate the prediction of unsaturated water conductivity (<italic>K(θ)</italic>). So, the purpose of the current investigation was to find out if a reliable relation or function between the two permeabilities can be established. In this regard, <italic>K(θ)</italic> and <italic>K</italic>_{<italic>a</italic>} were measured by pressure plate outflow and variable head methods, respectively, at the range of 0 to -100 kPa matric potential (<italic>ψ</italic>_{<italic>m</italic>}). A linear regression function between relative water conductivity (<italic>K</italic>_{<italic>r</italic>}(<italic>θ</italic>)) and <italic>K</italic>_{<italic>a</italic>} (<italic>LogK</italic>_{<italic>r</italic>} (<italic>θ</italic>)=<italic>a</italic>+<italic>bLogK</italic>_{<italic>a</italic>}) with the correlation coefficient (<italic>R</italic>) from 0.884 to 0.999 were established for the 22 examined soils. The overall <italic>R</italic> for 128 data pairs (<italic>K</italic>_{<italic>r</italic>}(<italic>θ</italic>) and <italic>K</italic>_{<italic>a</italic>}) became 0.821 (being significant at <italic>P</italic><0.01) with the slope (<italic>b</italic>) of -2.54 and intercept (<italic>a</italic>) of -10.93. For the comparison propose <italic>K</italic>_{<italic>r</italic>}(<italic>θ</italic>) were also predicted from RETC using experimental SMC data and van Genuchten and Brooks-Corey models. The reliability of the <italic>K</italic>_{<italic>r</italic>}(<italic>θ</italic>) prediction from <italic>K</italic>_{<italic>a</italic>} based on root mean square error (RMSE), geometric mean error ratio (GMER), and geometric standard deviation of error ratio (GSDER) criteria became considerable greater than those predicted from the two mentioned models.