A Self-adaptive Technique for Visualizing Geospatial Data in 3D With Minimum Occlusion

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Dec 11, 2013 (3 years and 7 months ago)

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A Self-adaptive Technique for Visualizing Geospatial Data in 3D With
MinimumOcclusion
Abon Chaudhuri and Han-Wei Shen
The Ohio State University,Columbus,OH,USA
ABSTRACT
Geospatial data are often visualized as 2D cartographic maps with interactive display of detail on-demand.Integration of
the 2Dmap,which represents high level information,with the details pertaining to specific locations is a key design issue in
geovisualization.Solutions include multiple linked displays around the map which can impose cognitive load on the user as
the number of links goes up,and separate windowed displays on top of the map which causes occlusion of the map.In this
paper,we present a self-adaptive technique which reveals hidden layers of information in single display and but minimizes
occlusion of the 2D map.The proposed technique creates extra screen space by invoking controlled deformation of the
2D map.We extend our method to allow simultaneous display of multiple windows at different map locations.Since
our technique is not dependent on the type of data to display,we expect it to be useful to both common users and the
scientists.Case studies are provided in the paper to demonstrate the utility of the method in occlusion management and
visual exploration.
Keywords:Geovisualization,3D Information visualization,Occlusion management,Computational geometry
1.INTRODUCTION
Geospatial data have become an integral part of modern life.As a result,analysis and visualization of such data have
emerged as an important research field.While novel techniques are regularly being proposed on the research front,related
software products such as map services,development libraries are coming up to enhance the scope for the scientists,
programmers and common users.
Speaking of visualization,the widely accepted style is to present geospatial data as a 2Dcartographic map,or to embed
it on a 3D virtual globe to be explored from a bird’s eye view.Depending on the data,a suitable attribute,for example
temperature or air pressure at each spatial location of the map,is used to create either a color or a height map.But in most
cases,encoding an attribute to color or height is not enough,since the information related to a spatial location is far more
complex.For example,temporal variation of an attribute (or multiple attributes) at each spatial location often comes as
an integral part of the data.In applications meant for common users,textual description or multi-media content such as
pictures,videos are often associated to spatial locations.Hence,extra screen space needs to be allocated to display such
information.
Different approaches exist to create extra roomfor displaying such secondary information.Multiple coordinated display
is one style where the user can select a point on the map to find the corresponding information highlighted on one or more
juxtaposed windows.However,as number of selection goes up,keeping track of the correspondence between the selected
locations and the visual element on other windows becomes difficult for the user.
Another popular approach is to have a new window popped up in response to the user’s click on a location.This
method,popularly used in many commercial tools as well,reduces the cognitive burden of linking a location to a point in
a remote window,since the spatial location is now tied to the window by a visible link.But Figure 1(a) suggests that this
method introduces a new concern,namely occlusion.A window can potentially occlude a considerable portion of the map
on background and also,some other windows.Several techniques can be employed to deal with occlusion:
1.Allowthe user to virtually fly around the location of interest and look at it fromall directions to reveal any potentially
occluded zone.But this technique clearly does not solve the problem,it just allows enough interactivity to shift the
occluded region fromtime to time.
Further author information:(Send correspondence to Abon Chaudhuri.)
Abon Chaudhuri:E-mail:chaudhua@cse.ohio-state.edu
(a)
(b)
Figure 1.Problem of occlusion on a map representing water el-
evation at the Amazon River Basin.(a) 2D windowed displays,
which presents temporal variation of water elevation at the se-
lected locations (located at the bottom left corner of each win-
dow),occlude the spatial map.(b) The problemof occlusion per-
sists when 3Dpop-up windows are allowed to stand on an oblique
map.
(a)
(b)
Figure 2.Two Google Earth snapshots to show current occlusion
management techniques.(a) Use of small suggestive icons.Oc-
casionally the icons can create visual clutter (shown in circled re-
gion).(b) Small icons may get occluded by expanded windows.
(a)
(b)
(c)
(d)
Figure 3.Semi-transparent windowas a solution of occlusion.(a) Overlaid 2Dwindows displaying time series.(b) Semi-transparent 3D
windows displaying time series.(c) Color-coded map of a region of interest.(d) Multiple semi-transparent color-coded maps overlaid
with each other.The blended color does not represent information accurately.
2.Use small suggestive icons which change to larger windows on mouse click.However,some regions of the map may
get cluttered due to many such icons (the circled region in Figure 2(a)) making the selection of a single one difficult.
Moreover,such small icons themselves are prone to get occluded behind larger windows (Figure 2(b)).
3.Limit the number of windows that can be displayed at a time.For example,some of the tools automatically close the
previous window when a new one appears under default setting.This strategy does not work when the user requires
wants to compare and analyze multiple regions.
4.Use semi-transparent window,which can be overlaid and blended on top of the 2D map.This method has two
limitations.Although the spatial map can be seen with moderate clarity through one semi-transparent layer,the
clarity reduces sharply as multiple windows overlap with each other (Figure 3(a) and Figure 3(b)).Secondly,if two
color-coded layers are blended with semi-transparency,the composite color does not reflect information properly.
So,if a portion of the map needs to be displayed with a different color scheme (possibly representing a different
variable or a different time step,as in Figure 3(c)),the window displaying this information should not be blended
with the map (Figure 3(d)).
5.Replace the rectangular windows by tall and thin shaped icons,
1
since they occlude each other to a much lesser extent
and can be easily spotted due to height.However,unlike rectangular windows which can be used for different types
of data,these icons provide non-standard visual spaces which may not be easily customized.Moreover,the user
needs to get familiarized with the structure each time a new type is encountered.
The above discussion summarizes the techniques,mostly ad-hoc in nature,which have been used with moderate success
to deal with occlusion.We introduce a new approach in this paper to significantly reduce occlusion by allowing the spatial
map to adapt its geometry based on user interaction.In our proposed method,when the user clicks on a particular location
or selects a region to visualize the secondary information associated,a window pops up in 3D and the 2D map distorts
to accommodate the pop-up.Ours is a novel screen space management technique,which smoothly integrates the 3
rd
dimension with the 2D-view to create overview+detail representation of geospatial data.
The primary benefit of the method is that the pop-up window does not occlude the background map.Also,the pop-up
windowstays adjacent (or very close) to its originating location.Hence,the user is spared of the burden of visually linking
two remote points.Moreover,our technique is generic enough so that it can be easily extended to display different types
of information.The benefits come at the cost of controlled deformation of the 2D map.But our technique provides quick
and smooth transition between the original undistorted view and the details view which makes it a considerable price.
Elevation-based occlusion management has been applied on treemaps,
2
where the deeper levels of a treemap are dis-
played in 3D without occlusion,by selectively elevating some rectangular blocks of the original treemap.Our proposed
method is different and tackles a harder scenario,since,unlike treemaps,geographic maps have no discrete components
and often contain features with no rigid boundary.Hence,abrupt changes of elevation would lead to discontinuity which
is not acceptable in this case (Figure 4(a)).Hence,our work takes up a different approach for modeling elevation.
The rest of the paper is organized as follows:Section 2 summarizes the research progress in related areas in recent
time.Section 3 introduces the proposed method,which is a blend of algorithm and visual design.Section 4 demonstrates
a few application scenarios that benefit fromour method,followed by a conclusive discussion in Section 5.
2.RELATED WORK
As geospatial data have grown in size and diversity over decades,the traditional cartographic representation of static 2D
maps has been improved with the aid of interactive graphics and visualization technology.Maps have evolved to being
active instruments or dynamic portals to interconnected,distributed,geospatial data resources.
3
One class of techniques has
worked on enhancing the visual representation aspect which always remains a fundamental issue,while another class has
focused on the data access and processing.Our work primarily deals with visual representation and models the behavior
of certain map objects in a novel way based on user interaction.
Map-based visualizations of geospatial data rely on color
45
or height mapping of values to present distribution of one
or more attributes
6
over the map.It has been shown
7
that clever use of visual properties such as hue and brightness can
effectively display temporal changes of spatial attributes.Another way of highlighting information through a spatial map
is to distort the map by encoding a spatial attribute to area or distance.The technique,primarily known as Cartogram,has
been thoroughly reviewed by Tobler
8
and applied to tools like Worldmapper.
9
Panse et.al.
10
have proposed pixel-based
techniques for spatial distortion of geographic map.Both these techniques were for purely 2D map though.A more recent
work
11
has shown controlled spatial distortion of a 3Dmap,seen from45

birds-eye view,to answer user-queries regarding
the best route between two geographic locations.
If the manipulation of geographic or color space of a map is only driven by data,it can potentially lead to cognitive
burden on the users.Such operations need to be guided by the principles of cartographic cognition,another important
aspect of map design.Related research by Olson,
12
Montello,
13
MacEachren
14
and many more has been instrumental in
understanding and modeling the human behavior with maps.
There are methods which allocate extra screen space for various types of secondary information.To avoid occlusion
of the map,this extra space is often created as separate window(s) which are co-ordinated with the map(as GeoVista
Studio
15
).Legible Cities
16
is an example which exploits multiple co-ordinated display for presenting spatially embedded
multi-dimensional data.Spatio-temporal data have also been visually explored with multiple co-ordinated displays in
17
.
18
If the windows appear at the corresponding selected locations (as in Google Map and Google Earth) on the map,
then occlusion becomes a serious concern which needs to be dealt with.Occlusion-centric research has been doone for 3D
geoscientific data as well.Occlusion-culling techniques
19
have turned out to be useful for 3Dvolume data with sub-surface
information layers.
A relatively recent survey of occlusion management techniques can be found at.
20
Based on theoretical understand-
ing of occlusion,a suite of metrics measuring occlusion
2122
has been proposed to enable comparison of traditional 2D
visualizations.Jittering
23
is an intuitive solution that reduces occlusion for a cluster of points on 2D.This basic strategy
of deforming the objects in visual space has been adopted in many ways.A recent work
24
has reduced occlusion in a
cityscape-like visualization of hierarchical data by deforming the bases of the 3D visual components.Similar techniques
can be found in geovisualization as well.To avoid occlusion caused by 3D map objects,route visualization algorithms
have introduced controlled distortion of landscape and/or map objects to make the route occlusion-free
25
.
11
However,these
algorithms are not directly applicable to our case.In general,they dislocate the 3Dobjects on the map to reveal the feature
of interest,namely the path of navigation.On the contrary,we address the challenge of retaining visibility of the entire
map in the presence of 3D objects.Moreover,we deal with occlusion caused by standing windows and not by geographic
features.This can be more challenging because rectangular windows are wide structures which stand orthogonal to the
viewdirection,causing a greater degree of occlusion.Also in our case,the rectangular windows should be able to showcase
information of any kind which stops us from freely deforming or rotating them.This distinction is important because in
other cases,the type of information conveyed though a map object is known in advance which may allow certain manip-
ulation on them.For example,there is information about each of the 3D boxes that represent buildings around a route of
interest.
There has been some work to deal with the type of occlusion presented in this paper.Thin and tall icons such as
Pencil-shaped or helical icons,
1
pin-shaped probes
26
and connected line segments
27
have been introduced as potential
replacements of rectangular windows.However,these approaches are not generic enough to be suited with any type of
information.On the other hand,our method allows placement of rectangle windows which can contain a all sorts of
information,ranging fromscientific data such as time series to personal content such as images,video clips.
3.PROPOSED METHOD
We propose a self-adaptive technique for visualizing detailed information associated with geographic maps without causing
significant occlusion of the map.Our technique creates suitable screen space for the detailed information to be displayed
on demand.Our technique is called self-adaptive because the rendering primitives (points,rectangles or triangles based
on implementation) constituting the spatial map automatically adjust their geometry and orientation to reveal the locations
potentially obstructed by one or more pop-up windows.
The spatial map we have dealt with is constructed from a 460 ×900 2D raster containing water elevation data of the
Amazon river basin for a single day.The dataset contains 300 temporal instances of the raster.In essence,each point
or spatial location on the map,identified by its row-column pair,is linked to a time series of daily water elevation to
be displayed on demand.However,the technique works irrespective of the exact nature of the information.Figure 4(b)
displays an example image of the map of Amazon River Basin.Broadly speaking,two types of interactions can be
(a)
(b)
Figure 4.(a) Problem of Discontinuity.Abruptly elevating only the occluded region causes discontinuity of the geographic map.(b)
Demonstration of the proposed occlusion reduction technique.The windowed display,referred to as infobox in this paper,presents the
temporal variation of water elevation at the bottom left corner of the window.The rear portion of the window has been elevated,with
continuity of the map intact.
expected on such datasets.The common users are likely to be more interested in local features,such as studying the time-
varying nature of the water elevation (for this map in particular) at locations near their residence or workplace.If adding
new data is allowed,they can also place landmarks at locations known to them or post pictures of places or architectures
around their residences.In short,the information added or requested by them are usually associated with one or a few
locations of the map.On the other hand,the statisticians or geoscientists are involved in studying one or more attributes
for a large region,if not the whole map.Hence,color-coded maps representing different attributes,or the same attribute
over a period of time,are of more interest to them.Our proposed technique is able to cater to the needs of both types of
users.
3.1 Overview
In our technique,a user interaction in the form of clicking a spatial location or selecting a rectangular region induces the
following course of events.A rectangular window which is perpendicular to the 2D map pops up.If the interaction is on a
single location,the window’s bottom left corner always stays on that location.If the user selects a rectangle,the window
stands along the farthest side of the selected region.From now on,infobox,a general name,will be used to refer to such
Figure 5.Potentially Occluded Regions.The 2D map can be con-
ceptually divided into regions based on how they are occluded
when an infobox appears (here in red,seen from top).When the
map is looked from bottom (front after it is tilted),region D (dark
gray) covers most of the occluded part,B and C (light gray) are
partially occluded,A (not shaded) is unaffected.
Figure 6.Sigmoid Function.The function used to model gradual
change of elevation in the transition regions.
pop-up windows.However,to enable clear view of the infobox,the 2D map needs to be tilted backward,so that its bottom
end comes towards the user and the top end moves away.The following pair of tasks is performed to reduce occlusion:
1.Identify the region of the map which will be potentially occluded by a pop-up window at a specific location.This
region is suitably elevated to avoid occlusion.
2.Determine the amount of elevation for each spatial point within the identified region and then,elevate each point
accordingly.
3.2 Identifying Occluded Regions
Figure 5 demonstrates (fromtop view) the extent of occlusion which an infobox (the thin red rectangle) of adequate height
can potentially cause.Assuming that the viewer at Eye is looking at the infobox frombottom (or,fromthe front when the
map tilts),the map can be conceptually divided into a few regions depending on the nature of occlusion.The front of the
infobox,namely region A,is unaffected.The rear,marked as region D,covers most of the occluded part.Regions B and C
include the rest.The extent of occlusion in regions B and C varies,but remains negligible compared to that in region D,as
long as the viewpoint stays to the bottom (front) of the map.Hence,imitating the approach described in,
2
we could have
elevated only region D to the height of the infobox,to obtain a visualization like Figure 4(a).But unlike a treemap which
consists of discrete rectangles,the features on a geographic map such as a river channel do not have a clear boundary.So
an abrupt change of height may obscure the features and hence,not acceptable.
Here is a closer look at the problem of discontinuity.If an infobox of height h appears at a point (r,c) and spans over
w columns (Figure 5),the points on row r +1 which are right behind the infobox must be separated by elevation h from
the points on row r which are right before the infobox.This much of discontinuity cannot be avoided since we place the
infobox between the rows.For the rest of the map,we model the change of elevation in such a way that the difference of
elevation for any two neighboring points remains negligibly small.
3.3 Elevation of Identified Regions
The motivation of this step is to increase the heights of the potentially occluded region as smoothly as possible when an
infobox of height h appears.A first look at Figure 5 suggests that region D needs to be elevated to height h and region A
does not require elevation at all.Hence,the problemboils down to gradually changing the elevation of points in regions B
and C from0 (at the bottom) to h (at the top).Fromnowon,region Dwill be referred to as the Upper Region and region A
as the Lower Region for convenience.Regions B and C are called Left and Right Transition Region.It can be also be noted
that each infobox gives rise to one of each of these four regions around it.
−10
−5
0
5
10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
The transition regions can be modeled in different ways as long as the change of elevation occurs smoothly.Apparently,
any s-shaped curve can guide a gradual change of elevation.We have employed a well-known curve called Sigmoid with
proper scaling factor to achieve this.Sigmoid function,which is expressed in many ways (Figure 6),can be defined
as f(x) =
1
1+e
−x
.Any other suitable candidate from a class of functions known as Logistic Functions can suitably
replace Sigmoid.From now on,we will use a general term S for this function.The exact formulation of S is left upon
implementation.When an infobox of height h and width w is requested at a point say P = (r,c),(Figure 7(a)) any point
(a)
(b)
Figure 7.(a) Modeling the Elevation.The upper,lower and transition regions along with their respective elevations.(b) The resulting
map fromthis elevation model has discontinuity which is exposed froma slightly side-wise rotated view.
that is below P falls in the lower region.The number of rows (vertical length) over which the transition regions should
span is a design choice.The more the number of rows,smoother is the change of elevation,but larger is the area under
distortion.We denote the length of transition region by d.So,any point which is above d rows from P falls in the upper
region with elevation h.Also,the points right above the infobox,between columns c and c+w,need to elevated by h.Rest
of the points between rows r and (r +d) belongs to the transition region.For a point in the transition region,the elevation
depends on the row number.The more a point has gone into the transition region,starting from the bottom,higher should
its elevation be.This can be formulated as S(m),where mis the normalized row distance measured relative to the bottom
end of the transition region.So,for a point P

with row number r

where r < r

< r +d,m= (r

−r)/d.
Figure 7(b) suggests that the above formulation of elevation map does not solve the problem of discontinuity com-
pletely.The problemappears in the inner part of the transition regions where they meet the infobox.To treat the inner parts
in a different way,we subdivide each transition region into two regions:one which is adjacent to the infobox on its both
sides and another,which is away fromthe infobox (Figure 8(a)).The region which stays away fromthe infobox is elevated
following the formulation already described.But the regions closer to the infobox,which may be called inner transition
regions,need further elevation in order to bridge the height gap.
The width of the inner transition region is another design choice.We denote the width by l.For a point at (r

,c

)
(Figure 8(a)),the additional elevation is denoted by a function F(m,n),where mand n are normalized row and column
distance relative to the boundary of the region.The normalized rowdistance m= (r

−r)/d is measured as the rowdistance
relative to the bottom.For the left (right) inner transition region,the normalized column distance n = (c

− c + l)/l is
computed relative to the left(right) boundary,where c −l < c

< c.It can be noted that for a point on row r

,the height
is S(m) and the height difference from the infobox is (h −S(m)).A new function is to be introduced here to gradually
compensate for this gap.For the rows which are closer to the bottom(denoted by low m),the rate of compensation should
be faster since the gap (h −S(m)) is larger.For the rows closer to the top (denoted by high m),the rate of compensation
should be slower.We have achieved this by a function F(m,n) of the formn
k
1
×(1−m)
×(h−S(m)),where the exponent
is controlled by the row position m,along with a constant k
1
.
To summarize,the elevation of a point in the transition region is denoted by S(m) and the elevation in the inner transi-
tion region is designed as S(m) +F(m,n) (Figure 8(a)).The resulting visualization of this elevation model (Figure 8(c))
reduces discontinuity to a negligible amount.
(a)
(b)
(c)
Figure 8.(a).Modified modeling of elevation.The transition regions are further divided into inner and outer transition regions.(b) The
inner transition region is distinctly shown before applying the elevation.(c) The resulting visualization minimizes the discontinuity to a
negligible amount.
3.4 Multiple Infoboxes
When more than one infoboxes appear,the above described strategy of four regions with different elevations should be
applicable to obtain a value of elevation for each infobox.And the final elevation for a point on the map should simply
be the addition of all such individual elevations.This simplistic strategy works except for a few cases (Figure 9(a)).The
problemoriginates fromthe fact that the inner transition region is,by definition,a surface with points of varying elevations,
since the elevation is dependent on both row and column ID of the points (last paragraph of Section 3.3).Suppose,an
infobox is requested at a point Q(Figure 9),which falls within the (left or right) inner transition region of an existing one
at P.Now,given the presence of an infobox at P,the new infobox cannot be erected right at Q.Many other situations like
this may occur,but in general,the problemsurfaces whenever the transition regions of two infoboxes overlap.
The overview of the proposed solution for the problem is illustrated in Figures 9(b) and 9(c).Given two infoboxes
with overlapping transition regions,the transition region which is relatively closer to the viewer can be safely merged into
the farther,without causing any occlusion (Figure 9(b)).In this particular example,the transition region of P has merged
to that of Q.P

denotes P after translation.A visual cue (a red line connecting P and P

in this case) is provided to
convey the changed location to the user.Merging of transition regions may give rise to another problem.If P

and Q
are close enough,the inner transition regions of one of them may overlap with that of the other (Figure 9(b)).So,the
widths of the overlapped inner transition zones need to be adjusted.In our implementation,the space between the two
infoboxes is equally divided between the two (Figure 9(c)).The following section provides an algorithmic approach to
these adjustments.
(a)
(b)
(c)
Figure 9.Schematic diagram of multiple infoboxes with overlapping transition regions.(a) Point Q falls in the inner transition region,
shaded in gray,of another point P.(b) The transition region of P is merged into that of Q.A visual link connects P with the relocated
infobox at P’.The right inner transition region of P’(gray) overlaps with the left inner transition region of Q(box with dotted boundary).
(c) The overlap is solved by dividing the space between the two infoboxes.Both transition regions now have equal space.
(a)
(b)
(c)
(d)
Figure 10.Visualization of 2D map with multiple infoboxes.(a) Single infobox.(b) A second infobox appears on the right and they
share the same transition region.(c) A third infobox appears whose transition region has no overlap with the existing one.(d)A fourth
infobox appears close to the third one.The third infobox is merged into the fourth one’s transition region.
3.4.1 Algorithmfor Multiple Infoboxes
A sequence of steps are to be taken to ensure that multiple infoboxes are placed properly without causing significant
occlusion.Let’s assume that N infoboxes,I
0
,...,I
n−1
are present at locations P
0
,...,P
N−1
.Each infobox corresponds to
a transition region T
i
.Suppose,a new infobox I
N
is requested by the user at P
N
.We assume that the infoboxes and the
corresponding transition regions are already sorted from front (bottom) to back (top).The task is to incorporate the new
one by adjusting positions of some of the existing ones,if needed.Steps to performthat are discussed below:
1.Compute the boundaries of the transition region T
N
for the new infobox.Insert I
N
and T
N
into the appropriate
positions of the respective sorted lists.So,at the end of this step,the list of infoboxes contains N +1 of them,along
with the corresponding N +1 transition regions.
2.Begin to scan each pair of consecutive infoboxes in the list such as I
0
and I
1
,I
1
and I
2
for possible overlap of their
respective transition regions.If two transition regions T
i
and T
i+1
are found to have an overlap,then merge T
i
into
T
i+1
.The infobox contained in T
i
should also move to T
i+1
.Hence,original T
i
is deleted,T
i+1
is now renamed
T
i
and it now contains two infoboxes (which were originally I
i
and I
i+1
).The indices of the subsequent transition
regions of the list are to be changed accordingly.After this merge operation is run through all the infobox pairs in
the list,the list contains,say k (where k ≤ N +1),transition regions T
0
,...,T
k−1
,where each transition region now
can contain one or more infoboxes.Under the new setting,the infoboxes contained in T
i
are denoted as I
i
0
,I
i
1
,...
etc.
3.The following and final step is to arrange the infoboxes within each transition region.Let us assume that transition
region T
i
contains p infoboxes I
i
0
,I
i
1
,...,I
i
p−1
,in order from left to right.Since the number of infoboxes in a
transition region is expected to be a reasonable number in all practical cases,this ordering step should not lead to
a major bottleneck.The next task is to scan through the ordered list of infoboxes and adjust the size of their inner
transition regions,if they are close enough to overlap.More specifically,given that the infobox width is w and the
inner transition region has width l,two infoboxes in the same transition region need to be at least 2 ×l +w distance
apart to have no overlap (Figure 11).If the distance is less than that,then the distance is equally divided between I
i
and I
i+1
.
The basic objective of all the above three steps is to re-compute the boundaries of transition (and inner transition) regions,
as needed.Once this is done,the elevation of each point on the map can be computed by using the formulae introduced
in Section 3.3.The same formulation is presented in Figure 12 with little changes made for multiple transition regions.
In the genral setting,if a point does not belong to a transition region,it should have an elevation of h times the number
of transition regions lying below it.If a point is in a transition region,an additional component of S(m) is to be added.
Finally,if the point belongs to an inner transition region,another additional component of F(m,n) is to be added further.
Figure 11.Two infoboxes in the same
transition region need to be at least 2 ×
l +w distances apart to have no overlap
between their inner transition regions.
Figure 12.Formula of elevation for multiple infoboxes.An example to show how different
regions of the map are to be elevated when more than one transition regions are present.
3.5 Self-adaptive Height of Infobox
In our technique,the user can tilt the 2D map backward to make the infoboxes visible.While exploring the infoboxes
which constitute the foci,the user can possibly lose the context information and want to restore the original 2D view of
the map.In such a case,as the user rotates back,the popped up infoboxes should not stand out as they would rapture the
original 2D map due to perspective projection.On the other hand,the infoboxes should not hide abruptly either.To avoid
such situations,the height of each infobox is set to vary in proportion with the angle of rotation or tilt of the spatial map.
2
As the user rotates the map by angle θ,the height should be θ ×k
2
,where k
2
is some constant.As a result,the height of
the infobox increases gradually with rotation and decreases smoothly as the user rotates in the reverse direction.
This is how our technique achieves smooth navigation between overview and detail.To have such a smooth and easy
transition is very important for our technique,because our method distorts,even though temporarily,some parts of the
overview to accommodate the detail.This ensures that as the user tilts the map backward,the distortion sets in gradually,
without rapidly breaking down the mental map already formed in the user’s mind.
4.CASE STUDY
4.1 Occlusion management
Geovisualization tools are often furnished with various data processing features such as querying,computing statistical
measures etc.Sometimes occlusion can impede accurate understanding of the data or the output from one or multiple
data processing tasks.The problem of occlusion becomes more severe when results from different tasks are integrated
and visualized on a single map,as shown in this case study.In our running example,we have implemented a basic data
processing:range query on normalized daily water elevation.The spatial locations containing attribute values within the
queried range are marked red.We also allow the user to query the temporal variation of the attribute at a single location.
The result of this query is presented on a pop-up window tied up to that location.Figure 13 demonstrates the role of
occlusion and the solution while presenting results of such queries.
In Figure 13(a),the range query result appears to have formed two clusters along the river channel.But when revisited
as a occlusion-reduced multi-level map in Figure 13(b),another cluster is revealed right behind the infobox which was
previously occluded.
Cognitive science research has shown that not only hiding objects,occlusion can also generate false impression of
objects.Figure 14(a) may lead to an impression that the queried range covers the entire river channel.However,the
alternate image shown in Figure 14(b) reveals the two discontinuities.
It can be argued that both the situations can be solved by simply rotating the map.But while observing the misleading
occluded maps which look complete,the user may not feel the requirement to rotate the map.Our technique provides the
motivation to further explore the hindsight of the infoboxes.
4.2 Comparative visualization
Human eyes can compare two things most effectively when they are placed next to each other.While analyzing time-
varying geodata,the user may be curious to knowhowa particular region will looks like in a different time step.Overlaying
is not suitable for this task and showing the other timestep in a different windowimposes cognitive burden on the user.Our
proposed technique allows that by placing infoboxes right on the map.The user can easily compare the present snapshot
of a region (on the main map) with its counterpart froma different time step (in the infobox).Optionally,the object in the
infobox can also be viewed as a mirror image of the original,since they share a common edge.Figure 15 shows how the
(a)
(b)
Figure 13.Case Study 1.(a) Two sections of the river channel appear to have fallen in the queried range.(b) A third section,right
behind the infobox,is revealed.
(a)
(b)
Figure 14.Case Study 2.(a) Apparently the queried range covers the entire river channel.(b) The previous inference turns out to be
erroneous when the occluded regions are revealed.
shape of a lake changes due to seasonal variation.In both Figure 15(a) and Figure 15(b),the region within red rectangle on
the basic map represents the lake at the current time step.The left infobox contains an image of the lake after 50 steps and
the right one is from 100 steps ahead of present.The mirror placement makes it easy to identify the most affected region
(the left corner of the lake).
(a)
(b)
Figure 15.The infoboxes can display temporal snapshots from
other time steps right beside the current map of the same re-
gion.The map from the other time step has been flipped as if
it is the mirror image of the original.This helps comparison
fromcognitive point of view.
(a)
(b)
Figure 16.Infobox employed to clutter reduction.(a) Visual clut-
ter caused by icons.(b) The deliberately introduced height differ-
ence reduces clutter,keeping the spatial location of each place-
mark intact.
4.3 Visual Clutter Reduction
Too many annotations or placemarks concentrated within a small region (Figure 16(a)) can clutter a map.Using our
technique,an artificial difference of elevation can be introduced through a region populated by placemarks (Figure 16(b)).
This simple technique disperses the placemarks and hence reduces clutter.
5.CONCLUSION AND FUTURE WORK
We propose a novel technique for reducing occlusion in Geovisualization.Our method achieves the goal by deviating from
the traditional cartographic map-plus-window style in many ways.For example,unlike windows that can be moved and
resized,our infoboxes are always rooted at the spatial map to provide better visual correspondence and to reduce cognitive
load.However,this spatial restriction does not prevent the windows from displaying different types of information.If
the dimension of the infobox turns out to be small for a particular application,zoom-in may be required to inspect the
details presented on the infobox.Zoom-in and zoom-out being the most frequently user interaction for geospatial data
which often comes in multiple resolutions,this should not stand as an additional burden to the user.Secondly,an infobox
distorts the map locally,but the distortion is temporary and can be undone at any moment using simple interaction such as
rotation.Arguably,the degree of distortion may prohibit too many infoboxes to appear simultaneously.But even if there
were no distortion,displaying so much information at the same time would not be effective anyway.In such a case,smaller
traditional icons,which can expand on-demand,can be used to replace some of the less important infoboxes.
The objective of this paper is to provide a means of data display with minimumocclusion,which can seriously impede
knowledge discovery in certain scenarios.Infoboxes can co-exist with traditional techniques such as landmarks,push-pins
and windows,hence incorporating our method as an additional feature into existing geovisualization systems should be
relatively easy.Another important aspect is that our method is oblivious to the nature (color,grayscale etc.) or content (the
type of data presented) of the data presented on the map.Hence,it is generic enough to be employed for exploration of
other types of 2D data such as remote sensing or medical images.
REFERENCES
[1] Tominski,C.,Schulze-Wollgast,P.,and Schumann,H.,“3d information visualization for time dependent data on
maps,” in [Information Visualisation,2005.Proceedings.Ninth International Conference on],175–181 (July 2005).
[2] Chaudhuri,A.and Shen,H.-W.,“A self-adaptive treemap-based technique for visualizing hierarchical data in 3d,” in
[Visualization Symposium,2009.PacificVis ’09.IEEE Pacific],105–112 (April 2009).
[3] MacEachren,“Research challenges in geovisualization,” Cartography and Geographic Information Science 28,3
(2001).
[4] Brewer,C.A.,“Color use guidelines for mapping and visualization,” Visualization in Modern Cartography,123–147
(1994).
[5] Dykes,J.and Brunsdon,C.,“Geographically weighted visualization:Interactive graphics for scale-varying ex-
ploratory analysis,” IEEE Transactions on Visualization and Computer Graphics 13(6),1161–1168 (2007).
[6] Olson,J.M.,“Spectrally encoded two-variable maps,” Annals of the Association of American Geographers 71(2),pp.
259–276 (1981).
[7] Shanbhag,P.,Rheingans,P.,and desJardins,M.,“Temporal visualization of planning polygons for efficient partition-
ing of geo-spatial data,” in [INFOVIS ’05:Proceedings of the 2005 IEEE Symposium on Information Visualization],
28,IEEE Computer Society,Washington,DC,USA (2005).
[8] Tobler,W.,“Thirty-five years of computer cartograms,” Annals of the Association of American Geographers 94(1),
pp.58–73 (2004).
[9] Dorling,D.,Barford,A.,and Newman,M.,“Worldmapper:The world as you’ve never seen it before,” IEEE Trans-
actions on Visualization and Computer Graphics 12(5),757–764 (2006).
[10] Panse,C.,Sips,M.,Keim,D.,and North,S.,“Visualization of geo-spatial point sets via global shape transformation
and local pixel placement,” IEEE Transactions on Visualization and Computer Graphics 12(5),749–756 (2006).
[11] Qu,H.,Wang,H.,Cui,W.,Wu,Y.,and Chan,M.-Y.,“Focus+context route zooming and information overlay in 3d
urban environments,” IEEE Transactions on Visualization and Computer Graphics 15(6),1547–1554 (2009).
[12] Olson,J.,“Cognitive issues in map use,” International Yearbook of Cartography 24,151–7 (1984).
[13] Montello,D.,“Cognitive map-design research in the twentieth century:Theoretical and empirical approaches,” Car-
tography and Geographic Information Science 29(3),283–304 (2002).
[14] MacEachren,A.M.,[How Maps Work:Representation,Visualization,and Design],The Guilford Press,1 ed.(June
2004).
[15] Gahegan,M.,Takatsuka,M.,Wheeler,M.,and Hardisty,F.,“Introducing geovista studio:an integrated suite of
visualization and computational methods for exploration and knowledge construction in geography,” Computers,
Environment and Urban Systems 26(4),267–292 (2002).
[16] Chang,R.,Wessel,G.,Kosara,R.,Sauda,E.,and Ribarsky,W.,“Legible cities:Focus-dependent multi-resolution
visualization of urban relationships,” IEEE Transactions on Visualization and Computer Graphics 13(6),1169–1175
(2007).
[17] Andrienko,G.and Andrienko,N.,“Visual exploration of the spatial distribution of temporal behaviors,” Information
Visualisation,International Conference on 0,799–806 (2005).
[18] Shimabukuro,M.H.,Flores,E.F.,de Oliveira,M.C.F.,and Levkowitz,H.,“Coordinated views to assist exploration
of spatio-temporal data:A case study,” Coordinated and Multiple Views in Exploratory Visualization,International
Conference on 0,107–117 (2004).
[19] Plate,J.,Grundh
¨
ofer,A.,Schmidt,B.,and Fr
¨
ohlich,B.,“Occlusion culling for sub-surface models in geo-scientific
applications,” in [VisSym],267–272,351 (2004).
[20] Elmqvist,N.and Tsigas,P.,“Ataxonomy of 3d occlusion management for visualization,” Visualization and Computer
Graphics,IEEE Transactions on 14,1095–1109 (Sept.-Oct.2008).
[21] Ellis,G.and Dix,A.,“The plot,the clutter,the sampling and its lens:occlusion measures for automatic clutter
reduction,” in [AVI ’06:Proceedings of the working conference on Advanced visual interfaces],266–269,ACM,
New York,NY,USA (2006).
[22] Brath,R.,“Metrics for effective information visualization,” in [INFOVIS ’97:Proceedings of the 1997 IEEE Sympo-
sium on Information Visualization (InfoVis ’97)],108,IEEE Computer Society,Washington,DC,USA (1997).
[23] Trutschl,M.,Grinstein,G.,and Cvek,U.,“Intelligently resolving point occlusion,” in [Information Visualization,
2003.INFOVIS 2003.IEEE Symposium on],131–136 (Oct.2003).
[24] Miyazaki,R.and Itoh,T.,“An occlusion-reduced 3d hierarchical data visualization technique,” in [IV],38–43 (2009).
[25] Takahashi,S.,Yoshida,K.,Shimada,K.,and Nishita,T.,“Occlusion-free animation of driving routes for car naviga-
tion systems,” IEEE Transactions on Visualization and Computer Graphics 12(5),1141–1148 (2006).
[26] Butkiewicz,T.,Dou,W.,Wartell,Z.,Ribarsky,W.,and Chang,R.,“Multi-focused geospatial analysis using probes,”
IEEE Transactions on Visualization and Computer Graphics 14(6),1165–1172 (2008).
[27] Kapler,T.and Wright,W.,“Geotime information visualization,” in [Information Visualization,2004.INFOVIS 2004.
IEEE Symposium on],25–32 (0-0 2004).