on the Gaussian scale-space representation by:
Orr May Mi Min ME}, GD)
l8z L«| ay Le|
where MF, = A qiiid MY, = Sra: ME, =
S ou leote? SS Joy?
£u: ad MS, — 7-51. 0. and 6, represent
the discrete first order deriatives on the horizontal and vertical
direction. Usually the features are extracted on a serie of scales
T= (t, to, ta, Da +
It has been shown in (Luo et al., 2008) that the image acquisition
process can be modelled by a Gaussian convolution followed by
a sampling. An image 7; of resolution r is obtained by:
IociLif sk. (4)
where II, is the sampling at resolution r, f is the continuous
function representing the scene, k-p is a Gaussian function with
standard deviation rp representing the MTF of the instrument, p
is the characteristic parameter of the MTF. The larger is p, the
smoother is the image. The Gaussian scale-space is scale invari-
ant.
According to (Luo et al., 2008), by using the causality of the
Gaussian convolution and Equations (2) and (4), we can obtain
the resolution invariance of the Gaussian scape-space features.
More concretely, the features extracted on the images of the same
scene with different spatial resolutions can be the same. More
concretely, for two images I, (with resolution 71) and I, (with
resolution 72) on the same scene, the features Oy .¢., and Oy yr,
extracted respectively on I, and I,., are equal, if
riv 0 -- p? — ra /t? + p2. (5)
It is shown in (Luo et al., 2008) that the resolution invariance of
the Gaussian waveletfeatures yields better indexing results than
using only the scale invariance of the Gaussian scale-space.
Therefore, for the images of two different resolutions 7; and r2,
we extract the features by Gaussian waveletat respectively two
series of scales T. — (11,15. 13,-.. and 7" — (0 15 s.l
and keep r14/t? -- p? — ra /t? + p?, the extracted features at
different resolutions can thus be compared for indexing.
2.2.2 Gray Level Coocurrence Matrix (GLCM) features The
Gray Level Co-occurrence Matrix computed on an image /, (with
resolution 7) is defined as:
PG. 1:65.65): T)
- 3 (a, y) (my) mi L(r s yoó)oj, ©
where # A represents the number of elements contained in the
set A. Usually, for an image I, four co-occurrence matrices are
computed at four orietations:
Lory = Ll: 3:4, 0:7) (7)
Poo;d;r = P(i, 3; 0, d;r) (8)
Pas;a,r = P(i,j;d, d;r) (9)
Prassar = Pli, 1. —d,—d:r). (10)
where d is the distance parameter. In this paper, 6 features (the
Angular Second Moment, the Contrast, the Variance, the Inverse
Different Moment, the Shadow of Clustering and the Prominence
of Clustering which are proposed in (Haralick et al., 1973)) are
respectively extracted from each matrix. The definitions of these
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B3, 2012
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia
features are shown in the Appendix. We note Hy 0.4.» (I = 1,2,... 14,
0 — 0, 90, 45, 135) the [th feature extracted on the GLCM Py.g4.,..
The GLCM feature set computed on an image /,. with resolution
r is defined as:
OÓdr = THtodr) (11)
where / — 1,2,...,6, 0 — 0,90, 45, 135. There are thus 4 x 6 =
24 GLCM features extracted for each image I.
For the indexing of images at different reslutions, we extract the
GCLM features from images with resolution r1 by using distance
d; and the GCLM features from images with resolution r2 by us-
ing distance d». Though equality between the GLCM features ex-
tracted on two images 7,4, and 7,» with two different resolutions
(but on the same scene) can not be rigorously established, we can
do a rough approximation between O ;z;4,,,, and Ozr:do:ra by
setting
di Xr = d» X T2. (12)
3 DATA SETS AND PARAMETERS
3.1 Data sets
The SPOTS image taken on the Nanjing, China is used. The
spatial resolution of the panchromatic image is 2.5m. Since the
SPOTS provides also multispectral data with 10m resolution on
the same region, we synthetize a panchromatic image with 10m
resolution by using the multispectral product in order to assure
the terrain types and the weather conditions are similar for the
classification for avoiding at most the influences of other factors
rather than the difference of the spatial resolutions.
The images are then cutted into small image patches. For the
images with the resolution of 2.5m, the size of each patch is
512 x 512 pixels; While for the reoslution of 10m, the size of
each patch is 128 x 128 pixels. Among all the image patches
of each resolution, 3 classes of terrains are chosen: the Build-
ing class (which contains 194 images representing the urban ar-
eas), the Vegetation class (which contains 194 images represent-
ing the forest areas) and the Farm class (which contains 202 im-
ages representing the rural and agricultural areas). In total, 670
image patches with 2.5m resolution and the same number of im-
age patches with 10m resolution are used for the classification.
Some examples of the image patches at different resolutions are
shown in Figure 1. It can be seen that even though the scene on
the ground is the same, the visual appearances (mainly the con-
trast) of the images at different resolutions are slightly different
(especially the images at the first column).
3.2 Parameters
Radiometric, texture and shape features are extracted from the
image patches for the experiments.
For extracting the Gaussian waveletfeatures, the parameter p (see
Equation (4)) is set to be 0.4, which is experimentally found to
be the most appropriate for the SPOTS instrument. For extracting
features from the images with 10m resolution, the scale param-
eters used are T' = (1.5; 2; 2.5; 3; 3.5; 4). The scale parameters
used for the images with 2.5m resolution are computed by using
Equation (5).
For extracting GLCM features, the GLCM at the four directions
(0, 45, 90, 135) are computed. For the image with 10m resolu-
tion, at each direction, the GLCM features of the distances 1, 2
and 3 are extracted. According to Equation (12), for the image
with 2.5m resolution, at each direction, the GLCM features of
the distances 4, 8 and 12 are extracted.
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