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ABOUT GRADIENT OPERATORS ON HYPERSPECTRAL
IMAGES
Ramón Moreno and Manuel Graña
Computational Intelligence Group, University of the Basque Country, San Sebastián, Spain
Keywords: Hyperspectral, Hyperspherical coordinates, Gradient, Chromatic Edge, Shadows.
Abstract: Gradient operators allow image segmentation based on edge information. Gradient operators based on
chromatic information may avoid apparent edges detection due to illumination effects. This paper proposes
the extension of chromatic gradients defined for RGB color images to images with n-dimensional pixels. A
spherical coordinate representation of the pixel's content provides the required chromatic information. The
paper provides results showing that gradient operators defined on the spherical coordinate representation
effectively avoid illumination induced false edge detection.
1 INTRODUCTION
Edge detection is a key step in some image
segmentation process. Edges are customarily
computed by applying linear gradient operators (i.e.
Sobel, Prewitt, Canny (Wang, 1997; Hildreth, 1987;
Gonzalez & Woods, 1992)). In color images,
gradients operators can be applied to each image
dimension independently, combining the results
afterwards. Alternatively, k-means clustering can be
applied to obtain color regions, defining the edges as
the boundaries of the found regions. The definition
of gradient operators on multi-dimensional pixel
images is an open research issue (Cheng, Jiang, Sun,
& Wang, 2001). Some approaches try to exploit the
properties of the color space (RGB, HSI, HSV, CIE
L*a*b, CIE L*u*v) to obtain sensible edge
detections. Chromatic gradient operators have been
proposed on the basis of the spherical representation
of the color points (Moreno, Graña, & Zulueta,
2010). Higher dimension images, hyperspectral
images, are becoming more common due to the
lowering cost of hyperspectral cameras, and the
growing number of airborne and satelite
hyperspectral sensors deployed by a number of
agencies. The issue of edge detection and the effect
of shadows and highlights is also open in this kind
of images. In many cases, shadows are hand
annotated in the remote sensing images to prevent
miss-segmentation. Chromaticity concepts have not
been extended to the hyperspectral image domain so
far, though they can be useful to improve
segmentation results. This paper proposes the
hyperspherical coordinate representation of the n-
dimensional Euclidean space (Moreno et al., 2010)
in order to introduce images. Hyperspherical
coordinate color representation allows to separate
chromaticy and intensity, the main colorimetrical
separation, without changing the image space. It is
therefore possible to extend Prewitt-like gradient
operators defined on the image pixels' chromaticity
(Moreno et al., 2010) to the hyperspectral case.
Those operators are independent of the image
luminosity, avoiding false edge detection on
highlights and shadows in the hyperspectral case.
This paper is outlined as follows: in Sec. 2 we
discuss about the Hyperspherical coordinates, giving
in 2.1 the transformation from Euclidean coordinates
to Hyperspherical coordinates. After that, in Sec. 3
we discuss about gradients, and in Sub-sec.3.1 we
will present a chromatic gradient operator. In Sec. 4
we will show the experimental results, finishing this
work in Sec. 5 with the conclusions.
2 HYPERSPHERICAL
COORDINATES AND
CHROMATICITY
An n-sphere is a generalization of the surface of an
ordinary sphere to an n-dimensional space. n-
Spheres are named Hyperspheres when
433
Moreno R. and Graña M..
ABOUT GRADIENT OPERATORS ON HYPERSPECTRAL IMAGES.
DOI: 10.5220/0003863904330437
In Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods (PRARSHIA-2012), pages 433-437
ISBN: 978-989-8425-98-0
Copyright
c
2012 SCITEPRESS (Science and Technology Publications, Lda.)