spatial ranking parameters for an internet-based remote sensing

ASPRS 2009 Annual Conference Baltimore, Maryland March 9-13, 2009

SPATIAL RANKING PARAMETERS FOR AN INTERNET-BASED REMOTE SENSING IMAGE BROWSING MECHANISM

Jung-Hong Hong, Zeal Su Department of Geomatics

National Cheng Kung University No.1 University Road, Tainan 701, Taiwan

[email protected] [email protected]

ABSTRACT With its superior capability to deliver abundant and instantaneous ground truth information, remote sensing image is highly regarded as the most popular data to support geospatial decision making. Recent internet technology innovation has dramatically reduced the difficulty of searching and accessing geographic data in distributed environment. For RS image users, the challenge is no longer “where to find images”, but “how to select the best image from the huge internet-based image archive environment.” This issue requires all of the candidate RS images to be “ranked” in a way to meet users’ application preference. Spatial constraint, i.e., the relationship between the AOI (Area of Interest) and RS images, is no doubt the most dominant factor during this selection process. From the spatial perspective, we proposed 3 indicators in this paper to serve as the basis for determining the spatial ranking of individual RS image with given AOI. Every indicator represents a mathematical formalization of users’ preferred scenario while selecting best images. These indicators are tested and analyzed extensively based on different dimensionality of AOI (point, curve, surface) to reflect its behaviors in different spatial layouts of AOI and images.

INTRODUCTION

A remote sensing image can record relatively large coverage of ground truth. With pixel resolution improved from 10m (SPOT Panchromatic) to 1m (IKONOS and QuickBird) and much easier availability via internet technologies, remote sensing images have evolved as an indispensable data source for referencing updated reality phenomena in GIS applications. With the introduction of commercial satellite platforms, remote sensing image data which was classified for government agencies only in the past has now been changed as a publicly accessible data source for everyone. Many large remote sensing image archives have been established and maintained over the past 3 decades (Charles and Dale and Nina, 2004). According to NASA RDS introduction (http://rsd.gsfc.nasa.gov/rsd/RemoteSensing.html), there are more than 50 categories of remote sensing image archives providing image access. And the USGS satellite land remote sensing data archive report (NSLRSDA, http://edc.usgs.gov/archive/nslrsda/dataarchivereport.pdf) also reveals a stunning fact about the incredible fast growing speed (terabyte per-day) in quantity and volume for USGS/EROS data and its derivative products (Behnke and Lake, 2000). Many internet-based applications and services have been established on the basis of RS image utilization such as GOOGLE EARTH and Microsoft VirtualEarth. Since images can deliver the most intuitive recognition and reflection of the real world, it is obviously inevitable evolving as the most popular spatial data resources in every aspect. With its stable and steady updates around the world, RS image arouses a revolutionary trend of being the representative of internet-based spatial data presentation. For the users from the cyberspace, more and more distributed RS image archives with rapidly increasing capacity and complex categories have become a new challenge to select those exactly appropriate images among tons of candidates. With the development and propagation of the internet technologies in the past, it has been a commonly granted principle that a reasonably ranked outcome shall be properly presented by the searching engines like the GOOGLE and YAHOO. Internet distributed archives all over the world collect and store global images according to categories and platforms. Any simple query may be responded with surprisingly large number of qualified images even if the user are experienced and expertized to know where and how to do it. Furthermore, users are very likely to give up browsing before they can reach the images. Main challenge for current RS image users has upgraded from searching to ranking. In order to calculate the ranking indicators, we adopted the ISO standardized elements generated directly with the image file


(resolution, temporal condition and ground registration coordinates) as the basis of discussion of this research. According to the natural characteristics of recording, each image’s extent of coverage represents its content. It’s content also represents users’ evaluation toward this image. Users will select image if it covers the area of interests (AOI). Events and phenomena analysis using RS image shall definitely base on if the it covers the location with acceptable spatial relation. Since the spatial constraint is undoubtedly the most crucial factor in users’ selection behavior, a quantitative indicator for spatial index measurements need to be discussed and developed for entire ranking mechanism. This paper focuses on the design, analysis and development of effective spatial ranking parameters. Four parameters are proposed in this paper. Each of them represents different subordination between the AOI and the candidate image on the basis of different quantitative measurements. Formalization for parameters will be discussed in this paper including the corresponding mathematical definition. Superiority and inferiority analysis for each parameter will also be discussed in this paper. A platform has been developed to emulate randomly distributed images and arbitrary polygon AOI. Experimental outcomes have revealed the consistency of harmonic tendency for each proposed parameters on evaluating each image. The outcomes also match users’ ranking expectation on the basis of proposed parameters.

LITERATURE REVIEW

Since it started from the demanding for exactly useful images by spatial ranking, we categorized four domains including image searching, image ranking, GEO-IR systems and component developments as the backbone of the following reviews. Fundamental spatial relations play a very important role as the foundation of spatial ranking. Egenhofer and Franzosa [1991] defined the well-known DE-9IM with 8 formalized spatial relations which construct the foundation of related researches. Mark, D. M., D. Comas, et al. [1995] proposed an effective way to evaluate and refine computational models of spatial relations. Beard,K. and V. Sharma [1997] proposed a multidimensional ranking mechanism for Alexandria Digital Libraries. They proposed a coverage-based spatial ranking scheme. It calculates the portion of the overlapping for specific spatial relations defined in DE-9IM. The multidimensional ranking is calculated graphically to inform users about how well data sets from a digital spatial library meet their spatial, temporal, and thematic targets. Since the spatial ranking indicator was defined by the portion of overlapping and non-overlapping coverage, it neglected the positional influences. For example, a point is contained in an image at different position which shall be granted different ranking. In image searching, Erwig, M. and M. Schneider [2002] proposed two methods to investigates temporal changes of topological relationships. Two-dimensional topological relationships and the change of spatial information over time are also discussed in this paper. It proposed a spatial predicates based searching method help in retrieving the GIS data during certain time intervals. It discussed the possible transitions among 2-D spatial predicates based on DE-9IM during developments and help users to retrieve qualified information. Janée, G. and J. Frew [2004] proposed two essential choices including (1) Allowable geographic representations (polygons with holes; collections of regions) (2) Allowable spatial query predicates (OVERLAPS, WITHIN, etc.) to regulate the image searching behavior in digital libraries. Jones, C. B., A. I. Abdelmoty, et al. [2004] introduced the S.P.I.R.I.T. search engine which proposed a geo-ontology based spatial-textual indexing for GIS data retrieval. It implemented a web-based test bed whose major components operating by extracted metadata and generated the relevance ranking by spatial relations summarized from geo-ontology hierarchies. In spatial ranking, Hjaltason, G. R. and H. Samet [1995] proposed an algorithm for ranking spatial objects according to increasing distance from a query object which is introduced and analyzed. The algorithm makes use of a hierarchical spatial data structure and its index in a spatial database. It proposed a quad-tree based methods generating the hierarchical ranking for specific queries. In GIR systems, Larson, R. R. and P. Frontiera [2004] proposed a method to evaluate the quality of geospatial approximations in GIR, i.e. how closely they represent the original objects, constrains how accurately and effectively these objects can be retrieved and ranked. This paper explored above issues and developed some new algorithms for ranked retrieval of geo-referenced objects. It also examined the indexing methods that can be employed for materials with geographic content or associations. We also reference a representative paper about the GEO-IR system implementing the image ranking mechanism. Kreveld, M. v., I. Reinbacher, et al. [2004] delivered an introduction about Geographic Information Retrieval (GIR) based on image metadata. It is concerned with retrieving documents in response to a spatially related query. This paper addresses the ranking of documents by both textual and spatial relevance. The distributed ranking means that the similar documents are ranked spread in the list instead of consecutively. The effect of this is that documents close together in the ranked list have less redundant information. This paper presents various ranking methods, efficient algorithms to implement them, and experiments to show the outcome of the methods on the basis


of metadata. Martins, B., M. J. Silva, et al. [2005] addressed documental indexing and retrieval using geographical location for digital libraries. It discusses possible indexing structures and result ranking algorithms, surveying known approaches and showing how they can be combined to build an effective Geo-IR system. About the ranking component we reference a famous paper as below. Markowetz, A., Y.-Y. Chen, et al. [2005] discussed the design and initial implementation of a geographic search engine prototype for Germany, based on a large crawl of the de domain. Geographic search engines provide a flexible interface to the Web that allows users to constrain and order search results in an intuitive manner, by focusing a query on a particular geographic region. Its prototype performs massive extraction of geographic features from crawled data, which are then mapped to coordinates and aggregated across link and site structure. It assigns to each web page a set of relevant URL locations, called the geographic footprint of the page and use it as the basis of ranking. The above reviews have demonstrated the spatial ranking for current systems (console databases or web-based digital libraries) adopting spatial relations as the backbone. Most of them constructed the ranking indicator by means of applying the extracted metadata items.

PROBLEM ANALYSIS

Cyberspace constructs a revolutionarily convenient environment for everyone to search and serve information. Simple keywords and few clicks may lead users to the answers which is hardly accessible in the past. Growing internet distributed archives continuously improve the availability for RS images. New technologies also bring new challenge to users to select correct and useful images from tons of candidates. According to the proposed image ranking framework, any qualified image shall meet 3 basic requirements: (1) The resolution (image platform) shall be fine enough for user to identify the AOI (2) The temporal attribute satisfies user’s temporal query (3)Image shall cover the entire AOI and maintain good relative position with it. The 3rd requirement is the fundamental principle of spatial ranking in image selection. In order to focus on the design and analysis of spatial ranking parameters in this paper, we propose two fundamental assumptions of constraint independence.

(1) Any image discussed in this paper satisfies user’s resolution constraint. It means images from different platforms shall not affect its spatial ranking result.

(2) Any image discussed in this paper satisfies user’s temporal constraint. It means images with different temporal attributes shall not affect its spatial ranking result. These two assumptions are used to simplify the analysis of the ranking outcome. It helps to make sure the

experiment outcome of the spatial ranking is representative for other two constraints. Image ranking involves two primary participants. One is the AOI (Area of Interest)—users can specify the reference objects and the available spatial relations according its dimensionality to composite the AOI. The definitions of the AOI follow the OGCSFS (http://portal.opengeospatial.org/files/?artifact_id=830). It defines the spatial object by its dimensionality including Point, Curve, Surface and their multiple type(MultiPoint, MultiCurve and MultiSurface). Another component is the image. We extracted the default extent element stored in metadata for each image. The extent can be expressed as a rectangle. In order to design effective spatial ranking parameters, we have to consider what kind of relation will be user preferences between AOI and image. Consequently, users will definitely use the AOI as the criterion to select images. No matter how images are produced, this fundamental prerequisite of coverage between the AOI and images shall be fulfilled for users to grant them. In this research we summarize three independent constraints for image selection. As for the resolution constraint, the AOI can be used to restrict acceptable resolution. For example, larger ground truth may be still identical in low resolution image. Yet smaller ground truth may be hardly identical in low resolution image at all. Therefore the acceptable resolution bounds shall be predefined from the size of the AOI for better recognition and interpretation. Furthermore, certain temporal relation shall maintain between the AOI and qualified images. It means the AOI shall exist while the image is generated. Generally speaking, corresponding temporal attributes for image and the AOI shall be expressed with different dimensionality, 0-D (time point) for image and 1-D( time interval) for the AOI. It can be expressed as the topological relations on the time axis (1-D) between the time points (0-D) and the time interval(1-D). If any time point representing an image is covered by the time interval representing the AOI, the image satisfies the temporal constraint. The third constraint is the spatial relations. The most intuitive consideration shall be if the candidate image can contain the entire AOI. Furthermore, the relative positions between each image and the AOI can be formalized and analyzed to define proper spatial priorities for candidate images. It is what we focus in this paper. Comparing with spatial constraint, the temporal and resolution constraints are relatively simple. According to the two assumptions of fixing the later two constraints, the spatial ranking result is the representative for image selection. The spatial relation between image and AOI can be described with 8 summarized relations proposed by Egenhofer and Franzosa in 1991. Likewise the boundary of an


image is denoted as , the other part inside the image is denoted as . The boundary of the AOI is denoted as and the other part inside the AOI is denoted as . The 8 relations including “Disjoint”, “Meet”, “Contains”,

“Covers”, “Inside”, “CoveredBy”, “Equal” and “Overlap” are used to define the spatial relations between the image and the AOI. Users nowadays can connect to distributed image archives via the internet. Plenty of image data resources users can turn to by the browser. There has accumulated considerable quantities of images covering most part of the world. Hence we restrict the qualified images shall completely cover the AOI. This is the fundamental threshold for images to be spatially ranked. According to the definition of the point-set theory, the relation can be explained as the inner part of the AOI and the image does intersect and the boundaries don’t. It can be expressed as ∩ ≠Φ, ∩ ＝Φ. Yet only 3 of the 8 relations can satisfy the definition including “Equal”, “Contains” and

“Covers”. It is almost impossible to find any image that can completely be equal in the coverage with the AOI. Consequently, our discussions will focus on the other two relations “Contains” and “overlap”. The two relations represent that the images can cover the AOI at least partially. It is obviously that images partially cover the AOI will not be ranked higher than those can cover the whole AOI. Since the ultimate purpose for image selection is to find the most useful image, complete coverage shall be the fundamental requirement in this paper. If all qualified images can completely cover the AOI, what relative coverage position might be better for users? According to the users’ expectations, if the AOI locates at the central part of an image shall be easier and clearer to interpret. Moreover, some users shall select images based on the additional information around the AOI. So if an image can cover the AOI in its central part means more additional information in every direction. Professionals will select images covering the AOI in their central part for minor relief displacement and radial distortion. It also grants better geometric precision and expandability for image based cartographic applications around the AOI. Consequently, we can summarize two user preferences for image selection from the above analysis:

(1) More additional information around and about the AOI (AOI shall be clearly identified in the image which satisfies the resolution constraint) from an image shall promise its priority in image selection. For example, the AOI (Taipei Main Station) are clearly demonstrated in these two images, the left one will be preferred than the right one because it can reveal not only sufficient information about the AOI but also more related ground truth around it.

(2) Better pictorial quality and geometric accuracy in central part of an image containing the AOI shall promise its priority in image selection. In the image below demonstrates the geometric distortion and relief displacement for Taipei 101 building away from the NADIR point in the image. We shall design effective spatial ranking parameters based on the above summarized preferences. Detailed

discussion for proposed parameters and corresponding implementations and experiments will be presented in the following sections.

QUANTITATIVE INDICATOR DEVELOPMENT

In order to deliver spatially ranked results, the above preferences form the basis of the following discussions. Each parameter will be defined and formalized in mathematical expressions and pseudo code. Corresponding behavioral analyses, pros and cons referring to variable dimensionality, positions and rotations are also included in the following sections.

Participants--AOI and Image Extent Introduction

Following the previous expositions, the AOI and the quadrangular coverage representing an image are expressed by the definitions in the OGCSFS. The AOI can be of the type “Point”, “Curve”, “Surface” and their plural forms (“MultiPoint”, “MultiCurve” and “MultiSurface”). For the plural form, we adopt the MBR (Minimum Bounding Rectangle) as the generalization and process the MBR as a “Surface” type. Since different type of image can record different ground truth details, we summarize several AOI considerations including dimensionality, shape, and direction dealing with the different ground coverage for each type of image to form the basis of discussions for the behavioral analysis for each proposed parameter.


Principles for Parameter Design In order to design effective parameters that can identify the correct spatial ranking among qualified images, two

quantitative indicators including area and length summarized from possible AOI-image spatial relation scenarios form the foundation of parameters. Since the AOI represents the spatial constraint, for every image containing the AOI may be granted with various ranking from its relative position, direction and proportion. Generally speaking, a useful image shall contain the AOI at first place. Other expectations such as proper resolution and AOI-image positions will follow one after another. All these expectations integrated and evolve as the two fundamental preferences on which we can induce the following six parameters for spatial ranking. The relations and considerations between parameters show in figure 1. Each proposed parameters is designed for different objective. Some of them are proportional and others are inverse proportional. The domain and range may vary contrarily. It may bring inconvenience for analyses and comparisons. In order to present a comprehensible outcome for the following discussions, a normalization transforming the ranges to (0,1) is necessary.

Figure 1. The correlations between parameters and considerations.

Since the two parameters “ADSS” and the “QS” show similar characteristics with the “IE” and “9GS” from the

outcomes in the experiments and also sensitive to the shape of the AOI, yet we adopt the other three parameters including “AS”, “IE” and “9GS” as the major ranking indicators in this research. We will define and formalize the three parameters and discuss the pros and cons. We also analyze the reactions and models for various AOI with different dimensionality, positions and rotations in experiments.

AS（Available Space）-- Auxiliary Information Buffering Around the AOI

Considering two images both completely containing the AOI, how can we decide which one shall be better? Since the complete containment of the AOI is the very fundamental spatial criteria for qualified image, we need another effective indicator to help in ranking images. Other than the information for AOI itself, we turn to the auxiliary information revealed around the AOI and take it as a new ranking indicator. It is impossible to have an image that can offer equivalent auxiliary information in every aspect around the AOI. Since we can never predict user’s preferred aspect around the AOI, we proposed a minimum distance method to generate the new indicator. Here is an example for a curve AOI generating the AS indicator demonstrated in Fig 3.


Figure 3. AS for Curve AOI.

Mathematic definition and formalized pseudo code. The definition of AS can be expressed as： P PointSet AO I.boundary and Q PointSet Im age.boundaryD = M in(D istance(Point_Pair(P ,Q )))

AS = AO I.Buffer(D )

∃ ∈ ∈ ∃ ∈ ∈∃

The starting point of designing the AS parameter is the additional information extended from the AOI. Under the threshold of complete containment of the AOI, qualified images can be ranked by the additional information extended from the AOI. According to the definition of AS parameter, we can determine the minimum distance from each node of the AOI to the four boundaries of an image and generate the buffer area with the minimum distance. The buffer area represents the available space (AS) and helps users to understand the ground truth around the AOI. The formal pseudo code for the implementation： For (i = 1; i<=n; i++) //n represents the total number of nodes For (j = 1; j<=4; j++) //4 boundaries

If (Distance(node(i), boundary(j)) < Min_distance) then //calculating distance Min_distance = Distance(node(i), boundary(j)); EndIf End for End for AS = AOI.Buffer(Min_distance); //calculating the buffer area (AS)

AS behavioral model analysis. The analysis involves AOIs of different dimensionality (POINT, CURVE and SURFACE). In order to clearly demonstrate the behaviors of parameters on different type of AOIs, we adopt the square grids as the experimental space and perform tests with equilateral and unequilateral AOIs of various positions and rotations. To implement the proposed test environment, a 100X100 square grids form the test space representing the extent of an image. The testee including a 0-D point, 2 1-D curves with different length (10, 20) and 2 2-D surfaces with different dimensions (10X10 and 10X30) represent AOIs of different dimensionality. In the tests we move and rotate the AOIs to emulate images with arbitrary AOI containment. The testee distribution graph is shown as figure 4. It demonstrates the AOIs of point, curve and surface type moving and rotating arbitrarily in the test space to analyze the behavioral models. In the following section, we will discuss how the positional and rotational variations affect AS’s behavioral model. We adopt the Sigmaplot® as the graphic tool to implement the corresponding 2D graphs and 3D models for following evaluations.

1:31:1

0-D (POINT)

1-D (CURVE)

2-D (SURFACE)

equilateralunequilateral

2010


Position variation effects analysis.

Figure 5. Position variation with different AOI dimensionality.

In figure 5.(a)AOI is a point, (b)AOI is a curve and its length is 10, (c) AOI is a curve and its length is 20, (d)AOI is a square, (e)AOI is a 1:3 rectangle. The graphs can prove no matter what type the AOI is (0-D, 1-D or 2-D) the AS will always be inversely proportional to the distance between the image center and the AOI. We can also discover contours for same AS value in the graphs. The AOI dimensionality will not affect the AS’s behaviors, different type of AOIs generate similar graph shape (graph (a),(b) and (d)). When the shape of the AOI changes (graph (b) and (c), (d) and (e)), the AS will demonstrate different characteristics since the shape change will affect the buffer distance. AOIs of different dimensionality may not influence the performance of the parameter. The major leading factor shall be the dimension of the AOI. The parameter answers to the dimensional changes in orthogonal direction. For example, if the AOI is vertically emphasized, t AS parameter is insensitive to the shifting in the horizontal direction.

Rotation variation effects analysis.

Figure 6. Rotation variations with different AOI dimensionality.

In figure 5. (a)AOI is a curve and its length is 10, (b) AOI is a curve and its length is 20, (c)AOI is a square, (d)AOI is a 1:3 rectangle. Rotation of the AOI will generate a totally different node distribution which changes the minimum buffer distance representing the AS. Periodic phenomenon occurs when the AOI rotates. For equilateral AOI ((c) in the figure 5.) the cycle is 90 degrees. For unequilateral AOI ((d) in the figure 5.) and line segments ((a) and (b) in the figure 5.) the cycle will be 180 degrees.

Conclusive characteristics for AS. As what we discussed in previous sections, the AS depends on the minimum distance from the AOI to the

boundaries. When the AOI locates right in the center of the image, it will generate the largest AS. If the AOI touches the boundaries of the image, the AS is 0. Since the AS is directly proportional to the minimum distance, complex shape will not change this tendency. Rotation of the AOI will affect the AS in a periodic manner. An equilateral AOI will have a cycle of 90 degrees. An unequilateral AOI will have a cycle of 180 degrees.

a b c d


Pros. 1. AS can directly reveal the exact buffer from minimum distance without any generalization and

simplification. It is comprehensible and intuitive. 2. Univariate presentation can be the primary indicator for ranking. Cons. Only the nearest boundary is considered to get the minimum distance, the other

three distances are neglected. It contains no information (position, distance) about the image center.Non-unique value for different scenarios may cause indeterminate ranking. Figure 7 shows two different positions with same AS value. AOI with ideal relative position and coverage may have bad AS if any node approaches the image boundary. Figure 8 shows the AOI with a node approaching to the boundary and have almost 0 AS. Image Extension Parameter

In order to neutralize the inevitable bias inherited from the AS parameter, we design the IE (Image Extension) parameter taking all distances to four boundaries into consideration to improve the differentiation. According to users’ expectation for an ideal image, a centrally located AOI is preferred scenario. Based on this demand, we extend the image to reset the MBR (Minimum Bounding Rectangle) of the AOI right in the center of the image by the differences of the horizontal and vertical distances from the MBR to the image boundaries. The figure 9 illustrates the generation of the IE parameter.The extended area (shaded in figure 9) also can be used to evaluate how the AOI approaching the image center. When the AOI approaches the image center, the extended area decreases and vice versa. We adopt the area ratio difference as the indicator. As the difference decreases, the AOI approaches the image center and vice versa.

Mathematic definition. Area of MBR Area of MBR

Area of original image Area of extended image

Ratio difference = −

Area of MBR Area of MBRArea of extended image Area of original image + Area of the extended part

ratio = =

Area of the extended part = ( - ) ( - ) ( ( ))Abs A B Y Abs C D X Abs A B× + × + − then Area of MBR Area of MBRratio difference

Area of original image Area of original image + Area of the extended part= −

Area of original image , = Area of extended part O E= , = Convex area of the AOIMBR

2

( )ratio difference ( )

MBR MBR MBR O E O MBR E MBRO O E O O E O OE

× + − × ×= − = =

+ × + +

A B

X

CD

Y

Abs(A-B)

Abs(C-D)

Figure 9. The definition of the IE.

Figure 8. Figure 7.


IE Positional variation analysis.

Figure 10. Positional variations with different AOI dimensionality.

In figure 10.(a)AOI is a point, (b)AOI is a curve and its length is 10, (c) AOI is a curve and its length is 20, (d)AOI is a square, (e)AOI is a 1:3 rectangle. We can summarize from figure 10 for AOI with different shape and dimensionality posses similar IE tendency. Comparing with the AS, it reduces the parametric duplicates and enhances the differentiation.

Rotational variation analysis. In figure 11, (a) represents the line of the length 20 and (b) represents the 1:3 unequilateral rectangles. We can see the rotation does not affect the IE parameter because the rotation may change the minimum distances to each boundary but the difference will remain constant.

Conclusive characteristics for IE parameter. 1. The difference remains 0 while the AOI locates right in the center of the image. It will produce the

minimum IE value. If the AOI approaches image boundaries, the parameter increases. 2. Shape of the AOI doesn’t affect the behavioral model of this parameter but the dimension of the AOI will

amplify the parameter. 3. Rotation doesn’t affect the parameter because the horizontal and vertical distance differences remain

constant in spite of rotation. Pros. 1. It involves all image boundaries measuring the corresponding distance differences and the correlation

between the AOI and the image center. 2. It is an univariate indicator that can complement the AS to improve the ranking. Cons. The IE parameter may demonstrate same value for symmetric positions in the

image because lacking of directional consideration.

Figure 11. Rotational variation for different AOI dimensionality.

Equal


9-gridding Square (9GS) Parameter In order to improve the shortcomings from the AS and IE parameters, we

propose a bivariate parameter to deal with the ranking for X and Y directions. As illustrated in the figure 14, we measure the A, B, C and D by enveloping the MBR of the AOI in the image. The IE parameter calculates the extended area by (A-B) and (C-D) to recenter the AOI in the image and the 9GS parameter adopts same information to evaluate the horizontal and vertical positions. In order to normalize and stabilize the range of the parameter, we introduce two indicators including atan(A/B) and atan(C/D) for horizontal and vertical positions respectively. For centrally contained AOI, the indicators reveal 45 degrees.

Mathematic definition.

Positional variation analysis. (1)ATAN(A/B)

In figure 15, (a) represents the point AOI, (b) represents a curve and its length is 10 (c) represents a equilateral surface (1:1). Since the indicator is designed to evaluate the horizontal changing, if the changes of the dimension take place in the vertical direction, this indicator will remain unaffected (contour graph for (a) and (b) in figure 15). Unlike the IE parameter, the indicator considers the ratio of A and B which will be affected by the dimensional changing.

(2)ATAN(C/D)

In figure 16, (a) represents the point AOI, (b) represents a curve and its length is 10 (c) represents a equilateral surface (1:1). The 9GS parameter is similar with the IE parameter which bases on the enveloping of the AOI and the atan of the corresponding differences. Its behavioral model is similar with the IE parameter and the shape of th AOI will not affect its outcomes. Similar with the atan(A/B) indicator, this indicator focuses on the vertical evaluation. It inherits identical characteristics discussed in the previous section.

A B

X

CD

Y


Rotation variation effects analysis. (1) ATAN(A/B)

In figure 17 (a)AOI is a curve and its length is 10, (b) AOI is a curve and its length is 20, (c)AOI is a square, (d)AOI is a 1:3 rectangle.

(2)ATAN(C/D)

In figure 18 (a)AOI is a curve and its length is 10, (b) AOI is a curve and its length is 20, (c)AOI is a square, (d)AOI is a 1:3 rectangle. Rotating AOI may change the enveloping and the corresponding distances to the image boundaries. It may affect the 9GS because its rotated shape. The affection can be categorized as a periodic phenomenon. For equilateral AOI, the period is 90 degrees. For line and unequilateral AOI, it’s 180 degrees.

Conclusive characteristics for 9GS parameter. Since the parameter are composed of the atan(A/B) and atan(C/D) indicators, yet their range defines from 0 to

90 degrees. No matter what kind of shape the AOI may be, the two indicators is 45 degrees when it is centrally contained in the image. If the AOI approaches the image boundaries, the two indicators are near 0 or 90 degrees. An unequilateral AOI may have substantial changes in its MBR while rotating. Therefore, an equilateral AOI may almost ignore the affections caused by rotation for its stable MBR.

Pros. 1. Two indicators are used to evaluate horizontal and vertical relative positions for the AOI respectively. The

differentiate ability is improved. 2. Considering two different perspectives including image center and boundaries. Cons. 1. Bivariate model may hampered the establishment of 1-D indicator. 2. The MBR is an essential ingredient for the parameter. When dealing with an AOI with complicated shape,

the center of the MBR may not coincide with the center of the AOI. Inaccurate outcome may occur.

Summary for Analysis We assign a 10X10 AOI moving along specific

direction in the 100X100 grids and calculate the parameters. Figure 19 demonstrates the changing tendency and comparisons for different directions. While the AOI moving along the orthogonal direction with the minimum distance defining the AS, the AS remains insensitive to the positional changes. Under this circumstance, the AS may not help. The IE parameter can help under similar situation. The 9GS uses two independent indicators for horizontal and vertical directional evaluations respectively. Integration for two indicators may achieve the effects like the IE parameter and help to define the necessary directional evaluation.

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Figure 19. Analysis summary.

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TEST AND RESULT ANALYSIS

In order to demonstrate the summarized characteristics and differentiability for proposed parameters (AS, IE and 9GS), we introduce seven representative scenarios as the trial templates to verify their performances. The validation involves AOIs of different dimensionality (point, curve and surface) completely contained in designed locations and inspects the parametric variations for different scenarios. Seven representative scenarios are proposed in figure 20. Each of them emulates different relation between the AOI and the image.

AOI

(A)

(B)

(C)

(D)

(E)

(F)

Figure 20. 7 scenarios for parametric validations.

According to the definition of the AS, scenario (A) and (B) shall lead to identical minimum values. The

comparison between scenario (A) and (B) instantiates a situation which is indecisive by the AS parameter but decisive by the IE parameter. The enveloping process while the IE parameter operates will simultaneously activate the 9GS parameter for directional evaluations. The scenario (C) and (D) is another example demanding for not only the AS parameter but also the IE parameter. The scenario (C), (D) and (E) explain that the IE parameter may be able to evaluate positional standing but is lack of the directional differentiability which needs to turn to the 9GS parameter. The scenario (F) stands for the ultimately ideal correlation between the AOI and the image leading to best outcome for every parameter. In order to display immediate parametric variations, we implement a platform being able to draw the corresponding graphics representing each parameter as shown in figure 21.

Figure 21. The test platform. Figure 22. Specifications for graphic display in platform.

Point AOI Scenarios and Corresponding Parametric Outcomes

Figure 23. Point AOI scenarios and corresponding parametric outcomes.


We can read from the figure about the ranking for AS parameter is（f）>（c）>（d）>（e）>（b）>（a）. Scenario (c) generates larger AS than scenario (d) and (e). Yet the AOI is contained in inferior position (distant from the image center) in the scenario. According to the discussion, a collaborative model for proposed parameters is feasible and inevitable to generate 1-D spatial ranking indicator.

Curve AOI Scenarios and Corresponding Parametric Outcomes

Figure 24. Curve AOI scenarios and corresponding parametric outcomes.

Surfacee AOI Scenarios and Corresponding Parametric Outcomes

Figure 25. Surface AOI scenarios and corresponding parametric outcomes.


CONCLUSIONS

A simple query can bring back a world of qualified images for complete containment of the AOI. A ranking mechanism is consequently necessary helping users by prompting commonly accepted sequence of priority. We propose several ranking parameters for evaluations on its spatial personalities for each qualified image in this paper. Corresponding examples displayed in the previous section can demonstrate correct tendencies for each proposed parameter in revealing and evaluating ranking in corresponding spatial aspects. Since the outcomes of designed experiments have proved the individual spatial differentiability, the next step shall head for a collaborative model for parametric integration to deliver an expectable and acceptable spatial ranking indicator. In order to integrate the three proposed parameters as an indicator, the parametric normalizations to rearrange the corresponding ranges is necessary. We had developed and implemented three different platforms to emulate, analyze and display the parametric tendencies for positional and directional variations. The next step forward shall lie in the independently integration for proper indicator referring to adequate ranges.

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spatial ranking parameters for an internet-based remote sensing

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