Often multidimensional data are visualized by splitting n-D data to a set of low dimensional data. While it is useful it destroys integrity of n-D data, and leads to a shallow understanding complex n-D data. To mitigate this challenge a difficult perceptual task of assembling low-dimensional visualized pieces to the whole n-D vectors must be solved. Another way is a lossy dimension reduction by mapping n-D vectors to 2-D vectors (e.g., Principal Component Analysis). Such 2-D vectors carry only a part of information from n-D vectors, without a way to restore n-D vectors exactly from it. An alternative way for deeper understanding of n-D data is visual representations in 2-D that fully preserve n-D data. Methods of Parallel and Radial coordinates are such methods. Developing new methods that preserve dimensions is a long standing and challenging task that we address by proposing Paired Coordinates that is a new type of n-D data visual representation and by generalizing Parallel and Radial coordinates as a General Line coordinates. The important novelty of the concept of the Paired Coordinates is that it uses a single 2-D plot to represent n-D data as an oriented graph based on the idea of collocation of pairs of attributes. The advantage of the General Line Coordinates and Paired Coordinates is in providing a common framework that includes Parallel and Radial coordinates and generating a large number of new visual representations of multidimensional data without lossy dimension reduction.
KEYWORDS: Stars, Visualization, Data modeling, Shape analysis, Feature selection, Visual analytics, Visual process modeling, Analytical research, Human vision and color perception, Statistical analysis
Although shape perception is the main information channel for brain, it has been poor used by recent visualization techniques. The difficulties of its modeling are key obstacles for visualization theory and application. Known experimental estimates of shape perception capabilities have been made for low data dimension, and they were usually not connected with data structures. More applied approach for certain data structures detection by means of shape displays are considered by the example of analytical and experimental comparison of popular now Parallel Coordinates (PCs), i.e. 2D Cartesian displays of data vectors, with polar displays known as stars. Advantages of stars vs. PCs by Gestalt Laws are shown. About twice faster feature selection and classification with stars than PCs are showed by psychological experiments for hyper-tubes structures detection in data space with dimension up to 100-200 and its subspaces. This demonstrates great reserves of visualization enhancement in comparison with many recent techniques usually focused on few data attributes analysis.
Correlating and fusing video frames from distributed and moving sensors is important area of video matching. It is especially difficult for frames with objects at long distances that are visible as single pixels where the algorithms cannot exploit the structure of each object. The proposed algorithm correlates partial frames with such small objects using the algebraic structural approach that exploits structural relations between objects including ratios of areas. The algorithm is fully affine invariant, which includes any rotation, shift, and scaling.
Automated Feature Extraction (AFE) plays a critical role in image understanding. Often the imagery analysts extract
features better than AFE algorithms do, because analysts use additional information. The extraction and processing of
this information can be more complex than the original AFE task, and that leads to the “complexity trap”. This can
happen when the shadow from the buildings guides the extraction of buildings and roads. This work proposes an AFE
algorithm to extract roads and trails by using the GMTI/GPS tracking information and older inaccurate maps of roads
and trails as AFE guides.
Geospatial data analysis relies on Spatial Data Fusion and Mining (SDFM), which heavily depend on topology and
geometry of spatial objects. Capturing and representing geometric characteristics such as orientation, shape, proximity,
similarity, and their measurement are of the highest interest in SDFM. Representation of uncertain and dynamically
changing topological structure of spatial objects including social and communication networks, roads and waterways
under the influence of noise, obstacles, temporary loss of communication, and other factors. is another challenge. Spatial
distribution of the dynamic network is a complex and dynamic mixture of its topology and geometry. Historically,
separation of topology and geometry in mathematics was motivated by the need to separate the invariant part of the
spatial distribution (topology) from the less invariant part (geometry). The geometric characteristics such as orientation,
shape, and proximity are not invariant. This separation between geometry and topology was done under the assumption
that the topological structure is certain and does not change over time. New challenges to deal with the dynamic and
uncertain topological structure require a reexamination of this fundamental assumption. In the previous work we
proposed a dynamic logic methodology for capturing, representing, and recording uncertain and dynamic topology and
geometry jointly for spatial data fusion and mining. This work presents a further elaboration and formalization of this
methodology as well as its application for modeling vector-to-vector and raster-to-vector conflation/registration
problems and automated feature extraction from the imagery.
As the availability of geospatial data increases, there is a growing need to match these datasets together. However, since
these datasets often vary in their origins and spatial accuracy, they frequently do not correspond well to each other,
which create multiple problems. To accurately align with imagery, analysts currently either: 1) manually move the
vectors, 2) perform a labor-intensive spatial registration of vectors to imagery, 3) move imagery to vectors, or 4) redigitize
the vectors from scratch and transfer the attributes. All of these are time consuming and labor-intensive
operations. Automated matching and fusing vector datasets has been a subject of research for years, and strides are being
made. However, much less has been done with matching or fusing vector and raster data. While there are initial forays
into this research area, the approaches are not robust. The objective of this work is to design and build robust software
called MapSnap to conflate vector and image data in an automated/semi-automated manner. This paper reports the status
of the MapSnap project that includes: (i) the overall algorithmic approach and system architecture, (ii) a tiling approach
to deal with large datasets to tune MapSnap parameters, (iii) time comparison of MapSnap with re-digitizing the vectors
from scratch and transfer the attributes, and (iv) accuracy comparison of MapSnap with manual adjustment of vectors.
The paper concludes with the discussion of future work including addressing the general problem of continuous and
rapid updating vector data, and fusing vector data with other data.
This paper presents the concept of Monotone Boolean Function Visual Analytics (MBFVA) and its application to the
medical domain. The medical application is concerned with discovering breast cancer diagnostic rules (i) interactively
with a radiologist, (ii) analytically with data mining algorithms, and (iii) visually. The coordinated visualization of these
rules opens an opportunity to coordinate the rules, and to come up with rules that are meaningful for the expert in the
field, and are confirmed with the database. This paper shows how to represent and visualize binary multivariate data in
2-D and 3-D. This representation preserves the structural relations that exist in multivariate data. It creates a new
opportunity to guide the visual discovery of unknown patterns in the data. In particular, the structural representation
allows us to convert a complex border between the patterns in multidimensional space into visual 2-D and 3-D forms.
This decreases the information overload on the user. The visualization shows not only the border between classes, but
also shows a location of the case of interest relative to the border between the patterns. A user does not need to see the
thousands of previous cases that have been used to build a border between the patterns. If the abnormal case is deeply
inside in the abnormal area, far away from the border between "normal" and "abnormal" patterns, then this shows that
this case is very abnormal and needs immediate attention. The paper concludes with the outline of the scaling of the
algorithm for the large data sets.
The methods used to evaluate automation tools are a critical part of the development process. In general, the most
meaningful measure of an automation method from an operational standpoint is its effect on productivity. Both timed
comparison between manual and automation based-extraction, as well as measures of spatial accuracy are needed. In this
paper, we introduce the notion of correspondence to evaluate spatial accuracy of an automated update method. Over
time, existing vector data becomes outdated because 1) land cover changes occur, or 2) more accurate overhead images
are acquired, and/or vector data resolution requirements by the user may increase. Therefore, an automated vector data
updating process has the potential to significantly increase productivity, particularly as existing worldwide vector
database holdings increase in size, and become outdated more quickly. In this paper we apply the proposed evaluation
methodology specifically to the process of automated updating of existing road centerline vectors. The operational
scenario assumes that the accuracy of the existing vector data is in effect outdated with respect to newly acquired
imagery. Whether the particular approach used is referred to as 1) vector-to-image registration, or 2) vector data
updating-based automated feature extraction (AFE), it is open to interpretation of the application and bias of the
developer or user. The objective of this paper is to present a quantitative and meaningful evaluation methodology of
spatial accuracy for automated vector data updating methods.
The variability of panchromatic and multispectral images, vector data (maps) and DEM models is growing. Accordingly,
the requests and challenges are growing to correlate, match, co-register, and fuse them. Data to be integrated may have
inaccurate and contradictory geo-references or not have them at all. Alignment of vector (feature) and raster (image)
geospatial data is a difficult and time-consuming process when transformational relationships between the two are
nonlinear. The robust solutions and commercial software products that address current challenges do not yet exist. In the
proposed approach for Vector-to-Raster Registration (VRR) the candidate features are auto-extracted from imagery,
vectorized, and compared against existing vector layer(s) to be registered. Given that available automated feature
extraction (AFE) methods quite often produce false features and miss some features, we use additional information to
improve AFE. This information is the existing vector data, but the vector data are not perfect as well. To deal with this
problem the VRR process uses an algebraic structural algorithm (ASA), similarity transformation of local features
algorithm (STLF), and a multi-loop process that repeats (AFE-VRR) process several times. The experiments show that it
was successful in registering road vectors to commercial panchromatic and multi-spectral imagery.
Robust imagery conflation, co-registration and geo-referencing are critical in many applications such as fusion of multispectral data from multiple sensors. An algorithm that matches linear features from two images can be very accurate because it produces many matched points, but the selection of robust and invariant points is a long-standing challenge. This paper defines several concepts of invariance and robustness of image matching algorithms relative to pairs of transformations. A new affine invariant and noise robust registration/conflation algorithm (EAD algorithm) based on algebraic structures of linear and area features is proposed. A class of Equal Area Divider (EAD) points is a major new component of the EAD-based registration/conflation algorithm. These points are both affine invariant and robust to noise. EAD points augment several known invariant or robust points such as Ramer point (R-point, the curve point with max distance from its chord), curve middle (CM) point and equal shoulders (ES) points that we have used in our structural algorithms previously. R point is affine invariant but is not noise robust, CM and ES are noise robust but not affine invariant. It is shown in this paper that if CM and ES points are computed after affine transform of the first image to the second one using EAD points, then CM and ES points are the same (or in the T-robust vicinity) of correct CM and ES points found in the matched feature in the second image. This statement is formalized and is used in EAD algorithm design.
KEYWORDS: Radar, Sensors, Filtering (signal processing), Detection and tracking algorithms, Neural networks, Global Positioning System, Infrared sensors, Data modeling, Monte Carlo methods, Electro optics
Integration of electro-optical and radar generated tracks is critical for identifying accurate time and space position information in target tracking and providing a single integrated picture (SIP) of the dynamic situation. This paper proposes a new, robust, real-time algorithm to (i) correctly correlate data from several sensors and the existing system track, (ii) improve target tracking accuracy and (iii) identify when the data represent new tracks. The proposed algorithm uses metric data, linear, and area features extracted from optical and radar images. The major novelty of the algorithm is in use of robust and affine invariant structural relations built on the features for accurate correlation. These features are combined with intelligent adaptation of Kalman filter using Neural Networks. A proposed measure of confidence with the correlation decision is based on both structural and metric similarities of tracks to estimate both bias and random errors. The similarities are based on concepts from the abstract algebraic systems, generalized Gauss-Markov stochastic processes, and Kalman filters for n-dimensional time series that explicitly model measurement dependence on k previous measurements, M(t/t-1,t-2,...,t-k). These techniques are naturally combined with the hierarchical matching approach to increase the overall track accuracy. The proposed approach and algorithm for track correlation/matching is suitable for both centralized and distributed computing architecture.
Complex challenges of optical imaging in diagnostics and surgical treatment require accurate image
registration/stabilization methods that remove only unwanted motions. An SIAROI algorithm is proposed for real-time
subpixel registration sequences of intraoperatively acquired infrared (thermal) brain images. SIAROI algorithm is based
upon automatic, localized Subpixel Image Autocorrelation and a user-selected Region of Interest (ROI). Human
expertise about unwanted motions is added through a user-outlined ROI, using a low-accuracy free-hand paintbrush.
SIAROI includes: (a) propagating the user-outlined ROI by selecting pixels in the second image of the sequence, using
the same ROI; (b) producing SROI (sub-pixel ROI) by converting each pixel to k=NxN subpixels; (c) producing new
SROI in the second image by shifting SROI within plus or minus 6k subpixels; (d) finding an optimal autocorrelation
shift (x,y) within 12N that minimizes the Standard Deviation of Differences of Pixel Intensities (SDDPI) between
corresponding ROI pixels in both images, (e) shifting the second image by (x,y), repeating (a)-(e) for successive images
(t,t1). In experiments, a user quickly outlined non-deformable ROI (such as bone) in the first image of a sequence.
Alignment of 100 brain images (25600x25600 pixel search, after every pixel was converted to 100 sub-pixels), took ~3
minutes, which is 200 times faster (with a 0.1=ROI/image ratio) than global auto-correlation. SIAROI improved frame
alignment by a factor of two, relative to a Global Auto-correlation and Tie-points-based registration methods, as
measured by reductions in the SDDPI.
A persistent problem with new unregistered geospatial data is geometric image distortion caused by different sensor/camera location. Often this distortion is modeled by means of arbitrary affine transformations. However in most of the real cases such geometric distortion is combined with other distortions caused by different image resolutions, different feature extraction techniques and others. Often images overlap only partially. Thus, the same objects on two images can differ significantly. The simple geometric distortion preserves one-to-one match between all points of the same object in the two images. In contrast when images are only partially overlapped or have different resolution there is no one-to-one point match. This paper explores theoretical and practical limits of building algorithms that are both robust and invariant at the same time to geometric distortions and change of image resolution. We provide two theorems, which state that such ideal algorithms are impossible in the proposed formalized framework. On the practical side we explored experimentally the ways to mitigate these theoretical limitations. Effective point placement, feature interpolation, and super-feature construction methods are developed that provide good registration/conflation results for the mages of very different resolutions.
We develop a software system Text Scanner for Emotional Distress (TSED) for helping to detect email messages which are suspicious of coming from people under strong emotional distress. It has been confirmed by multiple studies that terrorist attackers have experienced a substantial emotional distress at some points before committing a terrorist attack. Therefore, if an individual in emotional distress can be detected on the basis of email texts, some preventive measures can be taken. The proposed detection machinery is based on extraction and classification of emotional profiles from
emails. An emotional profile is a formal representation of a sequence of emotional states through a textual discourse where communicative actions are attached to these emotional states. The issues of extraction of emotional profiles from text and reasoning about it are discussed and illustrated. We then develop an inductive machine learning and reasoning framework to relate an emotional profile to the class "Emotional distress" or "No emotional distress", given a training dataset where the class is assigned by an expert. TSED's machine learning is evaluated using the database of structured customer complaints.
The problem of imagery registration/conflation and change detection requires sophisticated and robust methods to produce better image fusion, target recognition, and tracking. Ideally these methods should be invariant to arbitrary image affine transformations. A new abstract algebraic structural invariant approach with area ratios can be used to identify corresponding features in two images and use them for registration/conflation. Area ratios of specific features do not change when an image is rescaled or skewed by an arbitrary affine transformation. Variations in area ratios can also be used to identify features that have moved and to provide measures of image registration/conflation quality. Under more general transformations, area ratios are not preserved exactly, but in practice can often still be effectively used. The theory of area ratios is described and three examples of registration/conflation and change detection are described.
For multispectral sensory and geospatial data to be properly integrated they must be co-registered with known data which is a difficult and time consuming process. A persistent problem with new unregistered data is geometric image distortion. This paper deals with distortion due to disproportional transformation. Images can be disproportionally transformed because of a specific angle of data acquisition, sensor and lens distortions, atmospheric effects, and others factors. This research is focused on developing a method to overcome such distortion effects and to provide computational tools to automate a large portion of the process without relying on the sensor geometry and model that may not be known. Current methods of image analysis and feature recognition rely heavily on geometric shapes and/or the topological nature of data contained within the image. In addition to geometric shapes and topological data, features and images can also be compared algebraically. Algebraic structures have been defined with which comparisons can be made between geometric components such as relative angles, and lengths. Invariant point placement and feature comparison methods are developed here that can overcome the effect of distortion and disproportional scaling. Deriving a method that is invariant to disproportional scaling that is based on an algebraic invariant method is a new approach to solving this problem and represents a new mathematical language for the processing of image data.
The problems of imagery registration, conflation, fusion and search require sophisticated and robust methods. An algebraic approach is a promising new option for developing such methods. It is based on algebraic analysis of features represented as polylines. The problem of choosing points when attempting to prepare a linear feature for comparison with other linear features is a significant challenge when orientation and scale is unknown. Previously we developed an
invariant method known as Binary Structural Division (BSD). It is shown to be effective in comparing feature structure for specific cases. In cases where a bias of structure variability exists however, this method performs less well. A new method of Shoulder Analysis (SA) has been found which enhances point selection, and improves the BSD method. This paper describes the use of shoulder values, which compares the actual distance traveled along a feature to the linear distance from the start to finish of the segment. We show that shoulder values can be utilized within the BSD method,
and lead to improved point selection in many cases. This improvement allows images of unknown scale and orientation to be correlated more effectively.
An approach to conflation/registration of images that does not depend on identifying common points is being developed. It uses the method of algebraic invariants to provide a common set of coordinates to images using continuous chains of line segments formally described as polylines. It is shown the invariant algebraic properties of the polylines provide sufficient information to automate conflation. When there are discrepancies between the image data sets, robust measures of the possibility and quality of match (measures of correctness) are necessary. Decision making and the usability of the resulting conflation depends on such quality control measures. These measures may also be used to mitigate the effects of sensor and observational artifacts. This paper describes the theory of algebraic invariants and presents a conflation/registration method and measures of correctness of feature matching.
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