Kittipat Kampa

Closed-form cauchy-schwarz PDF divergence for mixture of Gaussians

This paper presents an efficient approach to calculate the difference between two probability density functions (pdfs), each of which is a mixture of Gaussians (MoG). Unlike Kullback-Leibler divergence (DKL), the authors propose that the Cauchy-Schwarz (CS) pdf divergence measure (DCS) can give an analytic, closed-form expression for MoG. This property of the DCS makes fast and efficient calculations possible, which is tremendously desired in real-world applications where the dimensionality of the data/features is very high. We show that DCS follows similar trends to DKL, but can be computed much faster, especially when the dimensionality is high. Moreover, the proposed method is shown to significantly outperform DKL in classifying real-world 2D and 3D objects, and static hand posture recognition based on distances alone.

Hurricane Response of Nearshore Borrow Pits from Airborne Bathymetric Lidar

Airborne bathymetric lidar surveys taken in Florida before and after the severe 2004 and 2005 hurricane seasons show infilling of seventeen dredged nearshore borrow pits. During these seasons, groups of pits captured volumes that were the equivalent of up to four years of net longshore transport, even though only one of the seventeen pits studied was inside the presumed depth of closure. Unsurprisingly, dimensionless infilling increased strongly with the ratio of wave height to pit depth. For open coast pits with large alongshore lengths, cross-shore infilling appeared to dominate over longshore infilling but both processes may be of comparable importance in shorter pits. Infilling of three borrow pits adjacent to ebb shoals was found to be considerably larger than on open coasts. Bathymetric changes in borrow pits occurred at greater depths than on nearby undisturbed profiles. Crude estimates of the long term infilling rates from tropical cyclones indicate that annual infilling volumes may be equivalent to more than one quarter of the expected net longshore transport at some locations. However, the episodic nature of hurricanes means that infilling events will be highly irregular.

Morphological segmentation of Lidar Digital Elevation Models to extract stream channels in forested terrain

Our paper proposes an approach for the extraction of stream channels from Airborne Laser Swath Mapping (ALSM) data. Recent advances in technology have led to high-resolution topographic data acquisition by means of airborne lidar (i.e. ALSM), which can yield Digital Elevation Model (DEM) datasets with horizontal resolutions of 1 m and vertical rms errors in the range of 10 - 15 cm. The extraction of a stream network from a DEM plays a fundamental role in modeling spatially distributed hydrological processes and flow routing. We apply morphological filtering to an ALSM DEM to detect and characterize stream channels in forested terrain. Since the size and shape of morphological Structuring Elements (SEs) is known to strongly affect filtered results, we test for accuracy by developing a set of error measures over simulated terrain. We subsequently apply the filter to actual ALSM data. For linking disconnected stream segments, a measure of pixel connectedness known as the Connectivity Number is used. The method presented is shown to enable systematic characterization and comparisons of streams, even in heavily forested terrain.

Irregular Tree-Structured Bayesian Network for image segmentation

Unsupervised image segmentation algorithms rely heavily on a probabilistic smoothing prior to enforce local homogeneity in the segmentation results. The tree-structured prior [1, 2, 3] is one such prior which allows important multi-scale spatial correlations that exist in natural images to be captured. Two main types of tree structure prior have been previously proposed: 1) fixed quadtree structure [1], which suffers from “blockiness” in the segmentation results and 2) flexible tree structure [2, 3] which can adapt its structure to the natural object boundary but at a significant computational cost. This paper presents a novel probabilistic unsupervised image segmentation framework called Irregular Tree-Structured Bayesian Networks (ITSBN) which introduces the notion of irregular tree structure that combines the merits of the two previous approaches. As in [2, 3], more natural object boundaries can be modeled in our framework since a tree is learned for each input image. Our method, however, does not update the adaptive structure at every iteration which drastically reduces the computation required. We derive a time-efficient exact inference algorithm based on a sum-product framework using factor graphs [4]. Furthermore, a novel methodology for the evaluation of unsupervised image segmentation is proposed. By integrating non-parametric density estimation techniques with the traditional precision-recall framework, the proposed method is more robust to boundary inconsistency due to human subjects.

Dynamic factor graphs: A novel framework for multiple features data fusion

The Dynamic Tree [1] (DT) Bayesian Network is a powerful analytical tool for image segmentation and object segmentation tasks. Its hierarchical nature makes it possible to analyze and incorporate information from different scales, which is desirable in many applications. Having a flexible structure enables model selection, concurrent with parameter inference. In this paper, we propose a novel framework, dynamic factor graphs (DFG), where data segmentation and fusion tasks are combined in the same framework. Factor graphs (FGs) enable us to have a broader range of modeling applications than Bayesian networks (BNs) since FGs include both directed acyclic and undirected graphs in the same setting. The example in this paper will focus on segmentation and fusion of 2D image features with a linear Gaussian model assumption.

Online learning using a Bayesian surprise metric

Dictionary.com defines learning as the process of acquiring knowledge. In psychology, learning is defined as the modification of behavior through training. In our work, we combine these definitions to define learning as the modification of a system model to incorporate the knowledge acquired by new observations. During learning, the system creates and modifies a model to improve its performance. As new samples are introduced, the system updates its model based on the new information provided by the samples. However, this update may not necessarily improve the model. We propose a Bayesian surprise metric to differentiate good data (beneficial) from outliers (detrimental), and thus help to selectively adapt the model parameters. The surprise metric is calculated based on the difference between the prior and the posterior distributions of the model when a new sample is introduced. The metric is useful not only to identify outlier data, but also to differentiate between the data carrying useful information for improving the model and those carrying no new information (redundant). Allowing only the relevant data to update the model would speed up the learning process and prevent the system from overfitting. The method is demonstrated in all three learning procedures: supervised, semi-supervised and unsupervised. The results show the benefit of surprise in both clustering and outlier detection.

Deformable Bayesian Network: A Robust Framework for Underwater Sensor Fusion

The dynamic tree (DT) graphical model is a popular analytical tool for image segmentation and object classification tasks. A DT is a useful model in this context because its hierarchical property enables the user to examine information in multiple scales and its flexible structure can more easily fit complex region boundaries compared to rigid quadtree structures such as tree-structured Bayesian networks. This paper proposes a novel framework for data fusion called a deformable Bayesian network (DFBN) by using a DT model to fuse measurements from multiple sensing platforms into a nonredundant representation. The structural flexibility of the DFBN will be used to fuse common information across different sensor measurements. The appropriate structure update strategies for the DFBN and its parameters for the data fusion application are discussed. A real-world example application using sonar images collected from a survey mission is presented. The fusion results using the presented DFBN framework are shown to outperform state-of-the-art approaches such as the Gaussian mean shift and spectral clustering algorithms. The DFBNs complexity and scalability are discussed to address its potential for a larger data set.

Bayesian surprise metric for outlier detection in on-line learning

Our previous work developed an online learning Bayesian framework (dynamic tree) for data organization and clustering. To continuously adapt the system during operation, we concurrently seek to perform outlier detection to prevent them from incorrectly modifying the system. We propose a new Bayesian surprise metric to differentiate outliers from the training data and thus help to selectively adapt the model parameters. The metric is calculated based on the difference between the prior and the posterior distributions on the model when a new sample is introduced. A good training datum would sufficiently but not excessively change the model; consequently, the difference between the prior and the posterior distributions would be reasonable to the amount of new information present on the datum. However, an outlier carries an element of surprise that would significantly change the model. In such a case, the posterior distribution would greatly differ from the prior resulting in a large value for the surprise metric. We categorize this datum as an outlier and other means (e.g. human operator) will have to be used to handle such cases. The surprise metric is calculated based on the model distribution, and as such, it adapts with the model. The surprise factor is dependent on the state of the system. This speeds up the learning process by considering only the relevant new data. Both the model parameters and even the structure of the dynamic tree can be updated under this approach.

Data-driven tree-structured Bayesian network for image segmentation

This paper presents Data-Driven Tree-structured Bayesian network (DDT), a novel probabilistic graphical model for hierarchical unsupervised image segmentation. The DDT captures long and short-ranged correlations between neighboring regions in each image using a tree-structured prior. Unlike other previous work, DDT first segments an input image into superpixels and learn a tree-structured prior based on the topology of superpixels in different scales. Such a tree structure is referred to as data-driven tree structure. Each superpixel is represented by a variable node taking a discrete value of class/label of the segmentation. The probabilistic relationships among the nodes are represented by edges in the network. The unsupervised image segmentation, hence, can be viewed as an inference problem of the nodes in the tree structure of DDT, which can be carried out efficiently. We evaluate quantitatively our results with respect to the ground-truth segmentation, demonstrating that our proposed framework performs competitively with the state of the art in unsupervised image segmentation and contour detection.

Dynamic trees for sensor fusion

The dynamic tree (DT) graphical model is a popular analytical framework for image segmentation and object classification tasks. A DT is a useful model in this context because its hierarchical property encodes information in multiple scales and its flexible structure fits complex region boundaries better than rigid quadtree structures such as tree-structured Bayesian networks. This paper proposes a novel framework for data fusion by using a DT model to fuse measurements from multiple sensing platforms into a non-redundant representation. The structural flexibility of the DT will be used to combine common information across different sensor measurements of simulated objects of interest. The appropriate structure of the DT and its parameters for the data fusion application are presented and discussed along with fusion results from a simulated sonar survey mission.