Shojiro Tanaka

Enhancement of low spatial resolution image based on high resolution-bands

Thermal infrared measurements of Band 6 acquired by Landsat TM sensor have lower spatial resolution than those of the other six bands. The authors propose a statistical approach to enhance the resolution of low spatial resolution image by using remaining bands. They employ a multivariate normal distribution for the seven band values. The values of Band 6 are predicted by the conditional expectations. Validity of their procedure is examined by mean squared errors based on actual images.

Accuracy and inaccuracy assessments in land-cover classification

Several measures assessing accuracy of land-cover classification are available, e.g., overall and class-averaged accuracies. Also the kappa statistic is widely used for this purpose. The authors discuss properties of these criteria and point out that the kappa statistic has an unfavorable feature. They propose an alternative coefficient based on Kullback-Leibler information. A test statistic for significance difference between coefficients is also established. Further, the Bayes risk, which takes types of misclassifications into account, is discussed. Their assessment measures are examined through actual error matrices by Z. Ma and R. L. Redmond (1995).

A Constant-Time Algorithm for Finding Neighbors in Quadtrees

Quadtrees and linear quadtrees are well-known hierarchical data structures to represent square images of size 2r times 2r. Finding the neighbors of a specific leaf node is a fundamental operation for many algorithms that manipulate quadtree data structures. In quadtrees, finding neighbors takes O(r) computational time for the worst case, where r is the resolution (or height) of a given quadtree. Schrack [1] proposed a constant-time algorithm for finding equal-sized neighbors in linear quadtrees. His algorithm calculates the location codes of equal-sized neighbors; it says nothing, however, about their existence. To ensure their existence, additional checking of the location codes is needed, which usually takes O(r) computational time. In this paper, a new algorithm to find the neighbors of a given leaf node in a quadtree is proposed which requires just O(1) (i.e., constant) computational time for the worst case. Moreover, the algorithm takes no notice of the existence or nonexistence of neighbors. Thus, no additional checking is needed. The new algorithm will greatly reduce the computational complexities of almost all algorithms based on quadtrees.

Modeling and inference of forest coverage ratio using zero-one inflated distributions with spatial dependence

This paper explores statistical modeling of forest area with two covariates. The forest coverage ratio of grid-cell data was modeled by taking human population density and relief energy into account. The likelihood of the forest ratios was decomposed into the product of two likelihoods. The first likelihood was due to trinomial logistic distributions on three categories: the forest ratios take zero, or one, or values between zero and one. The second one was due to a logistic-normal regression model for the ratios between zero and one. This model was applied to real grid-cell data and it fit better than zero-inflated beta regression models.

Verification of deforestation in East Asia by spatial logit models due to population and relief energy

Deforestation is a result of complex causality chains in most cases. But identification of limited number of factors shall provide comprehensive general understanding of the vital phenomenon at a broad scale, as well as projection for the future. Only two factors -- human population size (N) and relief energy (R: difference of minimum altitude from the maximum in a sampled area) -- were found to give sufficient elucidation of deforestation by nonlinear logit regression models, whose functional forms were suggested by step functions fitted to one-kilometer square high precision grid-cell data in Japan (n=6825). Likelihood with spatial dependency was derived, and several deforestation models were selected for the application to East Asia by calculating relative appropriateness to data. For the measure of appropriateness, Akaikes Information Criterion (AIC) was used. Logit model is employed so as to avoid anomaly in asymptotic lower and upper bounds. Therefore the forest areal rate, 0 < F < 1. To formulate East-Asian dataset, landcover dataset estimated from NOAA observations available at UNEP, Tsukuba for F, gridded population of the world of CIESIN, US for N, and GTOPO30 of USGS for R, were used. The resolutions were matched by taking their common multiple of 20 minutes square. It was suggested that data of full forest coverage, F=1.0, which were not dealt in calculations due to logit transformation this time, should give important role in stabilizing parameter estimations.

Nonlinear Regression Models to Identify Functional Forms of Deforestation in East Asia

Identification of the factors involved in deforestation could lead to a comprehensive understanding of deforestation on a broad scale, as well as prediction capability. In this paper, regression models with two explanatory variables-human population and relief energy, i.e., the difference between the maximum and minimum altitudes in a sampled area-were verified as to whether they could elucidate aspects of deforestation. The functional forms of the nonlinear regression models were estimated by step functions analyzed with the use of high-precision Japanese data. Candidate smooth regression models were then derived from the obtained sigmoidal shapes by the step functions. Models with spatially dependent errors were also developed. Akaikes information criterion was used to evaluate the models on four data sets for the East Asia region. From the evaluation, we selected the best three models that systematically showed the best relative appropriateness to the real data.

A model of deforestation by human population interactions

A differential equation was employed in modelling deforestation by human population interactions to yield an explicit mathematical model. The theoretical relation and many possible models were applied to the grid cell data in Hiroshima Prefecture, and relative appropriateness of each model was evaluated by Akaikes information criterion (AIC) using raw data. Intensive further verification was executed bythe bootstrap method. It was demonstrated that the theoretical relation was in the best agreement among many other models in comparison.

Statistical frameworking of deforestation models based on human population density and relief energy

This paper establishes a statistical framework of forest coverage models for spatio-temporal data. The forest coverage ratio of grid-cell data is modeled by taking human population density and relief energy as explanatory variables. The likelihood of the forest ratios is decomposed by the product of two likelihoods. The first likelihood discussed by Nishii and Tanaka (2010) is due to trinomial logistic distributions on three categories: the ratios take zero, one, or values between zero and one. We consider a precise modeling to the second likelihood for partlydeforested ratios by considering a) spline functions to the additive mean structure, b) wide spatial dependency of normal error terms, and c) an extended logistic type transform to the forest ratio. For spatio-temporal data, we implement auto-regressive terms based on the ratios observed in past. The proposed model was applied to real grid-cell data and resulted significant improvement compared to our previous model.

An application of novel zero-one inflated distributions with spatial dependence for the deforestation modeling

This paper considers statistical modeling of deforestation. Forest coverage ratio of grid-cell data was modeled by two covariates: human population density and relief energy. Conditional likelihood of the forest ratios given the covariates was decomposed by product of two likelihoods. The first one is due to trinomial logistic distributions on three classes: the ratios take zero, one or values between zero and one. The second one is due to a logistic-normal regression model for the ratios between zero and one. This model was applied to the real grid-cell data, and led remarkably interesting implications.

Deforestation due to population and relief energy through spatially-correlated logit models

Deforestation is a result of complex causality chains in most cases. But identification of limited number of factors shall provide comprehensive general understanding of the vital phenomenon at broad scale, as well as projection for the future. Only two factors - human population and relief energy (difference of minimum altitude from the maximum in a sampled area) - were found to give sufficient elucidation of deforestation by a regression model, whose functional forms were verified by linear combinations of dummy variables firstly explored with use of Japanese data. Likelihood with spatial dependency was derived and applied then to East-Asian data, with which our models showed the eminently good relative appropriateness to the real data.