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Module 8 Slant range to Ground rangeconversion

Program to run:sr2gr.m (bilinear interpolation),srogr_cubic_conv_2d.m (cubic convolution interpolation)

Functions used : -

Input : \module_7\multilooked_azi.dat

Output : sr2gr.dat (bilinear interpolation), srogr_cc.dat (cubic convolution interpolation)

Description :

!e "#$ and multi-looked images !ave slant range geometr% i.e. it is based on t!e actual

distance bet&een target and radar (in a direction &!ic! is at an angle'slant to t!e ground) not t!e

distance measured along t!e eart!s surace. e need to convert t!e slant range measurement

into t!e true ground range measurement so t!at all t!e eatures are in t!eir proper planimetric

(*,%) position relative to one anot!er in t!e inal radar image. !is is done b% resampling in range

direction. +n t!e program given in t!e module, sr2gr.m, bot! range and azimut! pi*els are

resized and resampled to get aground range image. un sr2gr.m to perorm slant range to

ground range image conversion on "#$ or azimut! multi-looked image along &it! bilinear

interpolation. un srogr_cubic_conv_2d.m to perorm slant range to ground range conversion

and interpolation b% cubic convolution met!od.

Explanation :

Slant range to ground range conversion:

"lant range to ground range conversion is also done in patc!-&ise manner. zimut!

resampling azimut! resampling is done b% orming indices in azimut! direction using t!e

ollo&ing relation.


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!ere r_inde* is t!e corresponding e*isting inde*, az_lookup is t!e ne& inde* arra% t!at

e*tends rom zero to number o azimut! lines in one patc!. !e ne&_size speciied can be

c!anged to var% t!e size in azimut! direction and also decides t!e size o az_lookup.

rg * Re

rg/ Re

ange resampling using t!e cosine la&, t!e ground range can be determined b% using t!e

relation

!ere !t is distance o sensor rom t!e center o t!e eart!, re is t!e radius o t!e eart! and ro is

t!at slant range distance. !is is calculated or t!e initial slant range. /rom t!is value o rg, t!e

ne&_size re0uired is added and slant range and corresponding ground range are iterativel%

calculated. "lant range calculation or a given ground range is done using t!e ollo&ing relation

!e ne& range lookup inde* is created iterativel% using t!e relation

2'1

2

2

2

2sincos

+=

baREarththeofRadius e


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ter t!is resampling is completed, interpolation is done. +nterpolation can be done in

several &a%s like bilinear interpolation, cubic convolution interpolation, cubic spline

interpolation etc. ilinear interpolation is used or resampling t!e input slant range image to get

ground range image. 3sing bilinear interpolation, t!e output pi*el value can be &ritten as

!ere zk is t!e value o t!e neig!boring pi*el and 4 k is t!e distance to t!at pi*el. !is results

in &eig!ting o t!e pi*els according to t!e distance rom t!e resampled point. !e output pi*el

value &ill depend on our neig!boring pi*els.

Cubic Convolution interpolation: cubic convolution is a pol%nomial interpolation met!od

based on convolution. !e &eig!ting is done in 5 * 5 &indo& in contrar% to t!e 2 * 2 in bilinear

interpolation. !e t!ird order cubic convolution kernel is given belo&.

!is is a one dimensional &indo&ing unction. !e 2-4imensional cubic convolution is

ac!ieved b% appl%ing t!is &indo& in t&o dimensions. o determine eac! pi*el value, &eig!ting

is applied or eac! o t!e 5 ro&s and t!en t!e same &indo& is applied to t!e 5 values obtained.


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Results:

Ground Range Image

Range bin

Azimuthbin

200 400 600 800 1000

100

200

300

400

500

600

700

800

900

1000

6round range image or ne& size in range and azimut! direction - 2


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Ground Range Image of Mumbai

200 400 600 800 1000

100

200

300

400

500

600

700

800

900

1000

1100

6round range image ater appl%ing cubic convolution interpolation

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