Jack D. Tubbs

A note on binary template matching

Abstract This paper considers some generalizations of binary template matching procedures which enable one to weight matches according to both statistical and spatial information.

Vertisol Carbonate Properties in Relation to Mean Annual Precipitation: Implications for Paleoprecipitation Estimates

Previous publications combining the properties of multiple soil orders show that depth to carbonate (DTC) increases systematically between 350 and 1000 mm of mean annual precipitation (MAP). We hypothesize that carbonate in Vertisols (clay‐rich, shrink‐swell soils) respond differently to water flux than other soil orders because of lower permeability. To test this hypothesis, we compiled soil description and characterization data from multiple published sources across a late Pleistocene climosequence of the coast prairie of Texas to assess the relationship between MAP (700–1400 mm) and DTC. The DTC of carbonate nodules represents an index of accumulation and the DTC of calcium carbonate equivalent (total carbonate <2.0 mm diam.) an index of leaching. The DTC for 1%, 2%, and 5% abundances were assessed using regression analysis. The R2 values were highest for the DTC of 2% nodules and of 1% calcium carbonate equivalent in Vertisol microlows. Surprisingly, relatively high R2 values were calculated for regression between MAP and DTC in Vertisol microhighs, whereby the relationship is expressed as a parabolic curve and DTC is shallowest in the central part of the climosequence where gilgai expression is greatest. When compared with previous MAP‐DTC relationships, it is clear that Vertisols retain carbonate into rainfall isohyets exceeding 1400 mm, >400 mm higher than the preservation of carbonate in other soil orders. When replotted, the use of DTC to estimate paleoprecipitation with previous equations underestimates MAP in a Mississippian paleo‐Vertisol microlow by approximately 32% at a DTC of 100 cm for 5% nodules. Other paleosol proxies also project greater rainfall than previous DTC equations in this paleo‐Vertisol.

A note on parametric image enhancement

Abstract A method for defining image enhancement operators based upon a parametric family is considered. This family of operators can be used for either context-free or context-sensitive enhancement that can be used either locally or globally. A modification of this procedure is suggested whereby the estimation of the parameters is performed using statistics which allow for efficient use of cellular or neighborhood image processors rather than those computed using the usual arithmetic operations.

Linear dimension reduction and Bayes classification with unknown population parameters

Abstract Odell and Decell, Odell and Coberly gave necessary and sufficient conditions for the smallest dimension compression matrix B such that the Bayes classification regions are preserved. That is, they developed an explicit expression of a compression matrix B such that the Bayes classification assignment are the same for both the original space x and the compressed space Bx . Odell indicated that whenever the population parameters are unknown, then the dimension of Bx is the same as x with probability one. Furthermore, Odell posed the problem of finding a lower dimension q p which in some sense best fits the range space generated by the matrix M . The purpose of this paper is to discuss this problem and provide a partial solution.

Pattern recognition of landsat data based upon temporal trend analysis

Abstract The problem of deciding whether or not a classification of a Landsat agricultural scene is acceptable when no ground truth is available was addressed. The approach taken was to examine temporal trends of the Landsat mean vectors of crops. A procedure for agricultural crop classification was developed using a time series (multitemporal) of Landsat mean vectors for selected agricultural fields in Montana and Kansas for which ground truth was known. This procedure using the temporal trend of mean vectors (the temporal trend procedure) was then applied to the individual Landsat pixels in more than one hundred multitemporal data sets collected throughout the wheat growing regions of the United States. The resulting classifications have compared favorably to ground truth estimates for proportion of wheat in those cases where ground truth was available. This temporal trend procedure has been found to give estimates of the wheat proportion that are comparable to the best results obtained using maximum likelihood classification with photointerpreter defined training fields. This classification scheme utilizing a temporal trend procedure is referred to as the “Delta Classifier”. It is currently being used as an independent, end-of-the-growing-season check on the reasonableness of maximum likelihood results in a quasi-operational Large Scale experiment (MacDonald et al., 1975).

Measures of confidence associated with combining classification results

The problem under consideration is that of combining classification results from several classifiers. This problem was motivated by the US Navys involvement in developing a system for integrating classification results from multiple sensors. As in any decision process one needs to quantify the uncertainty associated with the decision. A procedure based upon ranked lists from classification outputs is considered. Particular attention is given to the problem of assigning measures of confidence to the combined classification results where the interpretation is easily explained. >

A data-driven spline model designed to predict paleoclimate using paleosol geochemistry

Paleosols (fossil soils) are abundant in the sedimentary record and reflect, at least in part, regional paleoclimate. Paleopedology thus offers a great potential for elucidating high resolution, deep-time paleoclimate records. However, many fossil soils did not equilibrate with climate prior to burial and instead dominantly express physical and chemical features reflective of other soil forming factors. Current models that use elemental oxides for climate reconstruction bypass the issue of soil-climate equilibration by restricting datasets to narrow ranges of soil properties, soil-forming environments and mean annual precipitation (MAP) and mean annual temperature (MAT). Here we evaluate a data-driven paleosol-paleoclimate model (PPM1.0) that uses subsoil geochemistry to test the ability of soils from wide-ranging environments to predict MAP and MAT as a joint response with few initial assumptions. The PPM1.0 was developed using a combined partial least squares regression (PLSR) and a nonlinear spline on 685 mineral soil B horizons currently forming under MAP ranging from 130 to 6900 mm and MAT ranging from 0 to 27 °C. The PLSR results on 11 major and minor oxides show that four linear combinations of these oxides (Regressors 1-4), akin to classic oxide ratios, have potential for predicting climate. Regressor 1 correlates with increasing MAP and MAT through Fe oxidation, desilication, base loss and residual enrichment. Regressor 2 correlates with MAT through temperature-dependent dissolution of Na- and K-bearing minerals. Regressor 3 correlates with increasing MAP through decalcification and retention of Si. Regressor 4 correlates with increasing MAP through Mg retention in mafic-rich parent material. The nonlinear spline model fit on Regressors 1 to 4 results in a Root Mean Squared Error (RMSEMAP) of 228 mm and RMSEMAT of 2.46 °C. PPM1.0 model simulations result in Root Mean Squared Predictive Error (RMSPEMAP) of 512 mm and RMSPEMAT of 3.98 °C. The RMSE values are lower than some preexisting MAT models and show that subsoil weathering processes operating under a wide range of soil forming factors possess climate prediction potential, which agrees with the state-factor model of soil formation. The nonlinear, multivariate model space of PPM1.0 more accurately reflects the complex and nonlinear nature of many weathering processes as climate varies. This approach is still limited as it was built using data primarily from the conterminous USA and does not account for effects of diagenesis. Yet, because it is calibrated over a broader range of climatic variable space than previous work, it should have the widest array of potential applications. Furthermore, because it is not dependent on properties that may be poorly preserved in buried paleosols, the PPM1.0 model is preferable for reconstructing deep time climate transitions. In fact, previous studies may have grossly underestimated paleo-MAP for some paleosols.

An empirical sensitivity study of mixture proportion estimators

The sensitivity of several proposed estimators of the mixture proportions a = (a1,…,am)T defining the normal mixture density are investigated when the component densities pk are subjected to changes in location. The particular deviations studied are motivated by an application of this model to crop acreage assessment using satellite multispectral sensor data.

Effect of Autocorrelated Observations on Confidence Sets Based upon Chi-Square Statistics

How the presence of autocorrelation in a multivariate normal sample affects the confidence level of confidence regions based upon chi-square statistics is investigated. Particular consideration is given to the effect that this violation of the assumption of a random sample has upon the construction of confidence regions for the mean ¿ and the scalar ¿2, in ¿2V, where V is a known dispersion matrix.

Application of AUC Regression for the Jonckheere Trend Test

ABSTRACT A semiparametric regression model for the area under the ROC curve (AUC) is adapted to test of hypotheses for which the Jonckheere trend test (JTS) is appropriate. Since a nonparametric estimate of the AUC and the JTS depend upon the Mann-Whitney statistic, one can exploit this fact to develop a JTS that accounts for discrete covariates. The new method is illustrated with a simulation study and using real and simulated data motivated by three clinical studies.