www.geospatialworldforum.org

#GWF2020

7-9 April 2020 /// Amsterdam

Remote Sensing Applications

Images acquired from different satellites of same ground

coverage have different foot prints

Map overlay processing in Geographic Information System (GIS)

Computing an overlay of two vector maps to determine which

pairs of segments intersect.

Computer Vision

computing a partial 3D model of an environment from thousands

of partially overlapping photographs.

A casual photographer

turning overlapping photos into a single seamlessly stitched

panorama.

techniques for automatically discovering which images actually

form overlapping panoramas.

The following are some applications where overlap

area computation is most required in satellite

imagery

• GCPs and tie point identification in common regions.

• To select best pair of images from a database of images

in the given ROI.

• Mosaicking.

• DEM evaluation in the overlap region.

• Matching of images.

Overlap area computation between two images

Methods that use Image data

Spatial correlation

Matching technique

Methods based on geometrical aspects of foot prints

Analytical methods(integration)

Polygonal approximation

Domain Discretization Methods (Grid/Mesh)

Randomized Algorithms (Monte Carlo /Las Vegas)

When the foot prints have irregularly shaped boundary ?

Overlay of the foot prints of non Agile and Agile satellite images

17.4

17.45

78.4 78.45 78.5 78.55 78.617.1

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17.25

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17.35

Longitude

Lat

itud

e data1data2data3data4data5data6data7data8data9

or a combination of both…

In both the cases the overlap is between two regularly

shaped polygons with 4 sides.

Hence the overlap area is also a polygon.

It is now sufficient to find area of a polygon.

intersection of two polygons with 4 sides

common area between A

and B with points P1, A2,

P2, B0, with c as centroid of

common region.

Once the intersecting points are calculated, the required

area is the area inscribed in the polygon.

Area of a polygon with n sides,

say, (x1,y1), (x2,y2), …. (xn, yn)

is given by

17.4

17.45

17.5

Lat

itud

e (d

eg)

is given by

( )∑n

1i 1)n,imod(1)n,imod(

ii

yx

yxabs

2

1

= ++

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17.2

17.25

17.3

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Lontitude (deg)

Lat

itud

e (d

eg)

intersection points between A and B

Monte Carlo method to find overlap area between two 4-gons.

This method uses the random numbers uniformly spread out in A and

then searches for the points of A that are also in B.

The ratio of number of common points to the total points simulated in

region A multiplied by the area of A gives the common area.

R = [x , x ] × [y , y ]

Xmin Xmax

Ymax

Ymin

R = [xmin, xmax] × [ymin, ymax]

P(x∈A ∩ B) = P(x∈R) • P(x∈A|R) • P(x∈B|A∩R)

P(A ∩ B) = P(A) •P(B|A)

The conditional probability relationships between the initially sampled

rectangle region R = [xmin, xmax] × [ymin, ymax] and the area occupied by A in

this rectangle and then followed by area occupied by B in A are given in

sequence as P(x∈A ∩ B) = P(x∈R) • P(x∈A|R) • P(x∈B|A∩R) or simply P(A ∩ B)

= P(A) •P(B|A) since x is sampled from R.

where area(R) = ( ymax - ymin ) × ( xmax - xmin ).

The relative percentage of overlap between A and B is given by

area(B)*100/area(A).

This method is also very useful for finding areas of concave polygon regions by

suitably dividing them into appropriate convex sub regions.

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17.45

17.5

Lat

itud

e (d

eg)

An example of Overlap area calculation for carto-2 imagery.

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Longitude (deg)

Lat

itud

e (d

eg)

Figure: common points between A and B

In satellite imagery, irregularly shaped

boundaries/footprints are due to the following reasons

� Camera viewing geometry

� Curvature of the ground � Curvature of the ground

� Coverage of long passes

� Imaging over Polar regions

� Projection of the imaged area on to a plane.

A shape of double concave outline is shown in figure (1a),

and a sheared form of it is shown in figure (1b).

A case arises when imaging over the polar regions, if the spacecraft also

possesses roll movement then the corresponding imaged shape file

resembles like half the negative meniscus lens as shown in figure (1c),

High oblique images looks like figure (1d).

Few examples images acquired from TMC of Chandrayaan-1

Near Polar region

Nadir, Aft, Fore (Orbit No. 2488) Nadir, Aft (Orbit No. 2432)

Overlap area calculation

Analytical Method

Border coordinates are given in terms of latitudes and longitudes, say, (xi,yi)

Assuming that the closed shape bounded by four curves is approximated by

four polynomials of degree n of the form

where i = 1, 2, 3, 4. -----(1)

Perform a polynomial curve fit to the bounding curves of the footprint.

0

2n

2n

1n

1n

nn

ni a...αaαaαa)α(P ++++=

Perform a polynomial curve fit to the bounding curves of the footprint.

A D

P4 P2

EB CF

X=x2X=x1

P1

P

P3

••••

•••• ••••

••••

X

Y

Y=y2

Y=y1

∫∫P

dydxArea =

The overlap area enclosed in

the Region bounded by

two straight lines

Practically, two sides of the closed shape are bounded

by straight line as they correspond to the camera start

and end scan lines.

two straight lines

(y=y1, y=y2),

and two polynomials

( x=Q1(y), x=Q2(y) ),

given by

∫ ∫2

1

2

1

y

yy

)y(Q

)y(Qx

dydxArea= =

=

Different Cases of overlap region

Complexity increases with more number of intersecting points

Monte Carlo method to find overlap area between two shapes

This method uses the random numbers uniformly spread out in A and then

searches for the points of A that are also in B ( see figure ).

The ratio of number of common points to the total points simulated in

region A multiplied by the area of A gives the common area

80

85

90

Lo

ng

itud

e(d

eg)

ForeNadir

A case of TMC image of Chandrayaan-1, orbit No. 2522.

10 20 30 40 50 60 70

65

70

75

Latitude(deg)

Lo

ng

itud

e(d

eg)

NadirAft

Coverage of Nadir, Fore and Aft foot

prints of TMC image (orbit no. 2522)

40

45

50

55

Lat

itud

e(d

eg)

DataPolynomial Approx

35

40

45

50

55

60

65

Lat

itud

e(d

eg)

DataPolynomial Approx

Polynomial approximation of foot print boundaries

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35

Longitude (deg)

70 75 80 85 90

20

25

30

35

Longitude(deg)

Fore image foot print and its polynomial

approximation.

Nadir image foot print and its

polynomial approximation.

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45

50

55

60

65

65 70 75 80 85 9020

25

30

35

the overlap area calculation between Nadir

and Fore shape files for N=5000 simulations.