A generalized adaptive mathematical morphological filter for LIDAR data

Airborne Light Detection and Ranging (LIDAR) technology has become the primary method to derive high-resolution Digital Terrain Models (DTMs), which are essential for studying Earth's surface processes, such as flooding and landslides. The critical step in generating a DTM is to separate ground and non-ground measurements in a voluminous point LIDAR dataset, using a filter, because the DTM is created by interpolating ground points. As one of widely used filtering methods, the progressive morphological (PM) filter has the advantages of classifying the LIDAR data at the point level, a linear computational complexity, and preserving the geometric shapes of terrain features. The filter works well in an urban setting with a gentle slope and a mixture of vegetation and buildings. However, the PM filter often removes ground measurements incorrectly at the topographic high area, along with large sizes of non-ground objects, because it uses a constant threshold slope, resulting in "cut-off" errors. A novel cluster analysis method was developed in this study and incorporated into the PM filter to prevent the removal of the ground measurements at topographic highs. Furthermore, to obtain the optimal filtering results for an area with undulating terrain, a trend analysis method was developed to adaptively estimate the slope-related thresholds of the PM filter based on changes of topographic slopes and the characteristics of non-terrain objects. The comparison of the PM and generalized adaptive PM (GAPM) filters for selected study areas indicates that the GAPM filter preserves the most "cut-off" points removed incorrectly by the PM filter. The application of the GAPM filter to seven ISPRS benchmark datasets shows that the GAPM filter reduces the filtering error by 20% on average, compared with the method used by the popular commercial software TerraScan. The combination of the cluster method, adaptive trend analysis, and the PM filter allows users without much experience in processing LIDAR data to effectively and efficiently identify ground measurements for the complex terrains in a large LIDAR data set. The GAPM filter is highly automatic and requires little human input. Therefore, it can significantly reduce the effort of manually processing voluminous LIDAR measurements.

Statistical analysis and optimal classification of blood cell populations using Gaussian distributions

This dissertation develops a new figure of merit to measure the similarity (or dissimilarity) of Gaussian distributions through a novel concept that relates the Fisher distance to the percentage of data overlap. The derivations are expanded to provide a generalized mathematical platform for determining an optimal separating boundary of Gaussian distributions in multiple dimensions. Real-world data used for implementation and in carrying out feasibility studies were provided by Beckman-Coulter. It is noted that although the data used is flow cytometric in nature, the mathematics are general in their derivation to include other types of data as long as their statistical behavior approximate Gaussian distributions. ^ Because this new figure of merit is heavily based on the statistical nature of the data, a new filtering technique is introduced to accommodate for the accumulation process involved with histogram data. When data is accumulated into a frequency histogram, the data is inherently smoothed in a linear fashion, since an averaging effect is taking place as the histogram is generated. This new filtering scheme addresses data that is accumulated in the uneven resolution of the channels of the frequency histogram. ^ The qualitative interpretation of flow cytometric data is currently a time consuming and imprecise method for evaluating histogram data. This method offers a broader spectrum of capabilities in the analysis of histograms, since the figure of merit derived in this dissertation integrates within its mathematics both a measure of similarity and the percentage of overlap between the distributions under analysis. ^