igarss 2002 craters poster 3 - portland state...

IntroductionThe recognition problem is of great importance in all situationswhere automatic decisions must be made without the interventionof the man. Recognition is one of the most studied problems incomputer vision.

Recognition in Remote SensingIn computer vision applications the image data are characterizedby low level of white additive noise and distortions due to thecamera, while the object searched has sharp edges and a wellidentified shape.

In remote sensing applications, in addition to the fact that theimages are corrupted by different types of noise or distortions,often the features of the object searched itself cannot be welldefined, or his outlines can be known only with a poorapproximation.

Automatic recognition can allow to analyze the larger and largeramount of remote sensing data available.

Main Recognition MethodsDifferent techniques have been developed for recognition ofobjects. Two important families are the matching algorithms andthe voting techniques. Matching algorithms use a copyopportunely simplified (template including the more relevantfeatures) of the object to be detected. In voting techniques aschematic shape model of the object is used. Our approch tocraters recognition uses the Hough Transform (a voting technique)modified with significant improvements.

Hough TransformThe Hough transform can be considered the discrete version of the Radon transform. Letz=f(x,y) be a 2D signal defined on a domain A. Given a parametric curve g(x, y; p1, p2 ,..,pk),we define the Radon transform as the transformation between the space A and the space ofparameters R2 in this way:

where δ(∗) is the Dirac function.

The Hough Transform is based on the the idea of building a parameter space where thedetection is computationally easier. The fundamental algorithms consists of three basic steps:•One pixel of the image space is transformed into a curve in the parameter space•The parameter space is divided in cells. Each pixel of the image give one score to the cells lying on thetransformed curve.•The cell with maximum scores is selected and its coordinates in the parameter space are used to identify thecurve to be found in the image space.

dxdypppyxgyxfpppf kk )),,,,,((),(),,,( 2121 ∫ ∫ ⋅= δ

Feature SpaceAn important step, in the recognition process, is the definition ofthe object to be detected. A representation of this object can bemade only by using an ideal model that includes the mostrelevant discriminating features. Information characterizing themodel of the object to be recognized is entirely contained in theFeatures Space.

Hough Transform for straight lines

On planet images, craters can be detected quite easily.Automatic recognition can allow comprehensive planetsurface surveys (Mars, Moon,..)

Interplanetary Applications:Test on Mars images

Scaling TechniqueIt is important to introduce a method to scale the cells of the parameter spacedepending on the radius values, that is a non-uniform sampling of the parameterspace.

∆∆∆∆r, ∆∆∆∆x and ∆∆∆∆y define the sizeof a single cell in the parameterspace and characterize theadmitted errors on the radiusand center values. Differenttests suggest to scale thevolume of the cells linearlywith the radius: ∆x ∆y ∆r ~ r

∆y

∆x

∆r

Parameter space “resolution”By reducing the parameter space “resolution” as the radius increases it is possible toimprove the detection of particularly corrupted shapes (and to reduce the size of theparameter space).

A shape is recognized as a circlewhen the shape fits a perfect circlewith an error ∆r=f(r) that is anincreasing function of the radius:larger circular structures admit aradius error ∆r higher than smallcircles.

r

r + ∆r

Proposed Improvements

Craters on the Earth:detected craters ontest imagesAid tool for recognition of craters. Onthe Earth surface, recent or wellconserved craters have an evidentcircular shape, while old and verydegraded craters are oftencharacterized by complex concentriccircular patterns. The proposedalgorithm showed promising resultsfor recognition of both kind of craters.The Aorounga and Talemzane are twovery different examples of craters onthe Earth. Aorounga crater, Chad Talemzane crater, Algeria

Mario Costantini,1 Massimo Zavagli,2 Mario Di Martino,3 Pier Giorgio Marchetti,4 and Franco Di Stadio1

E-mail: mario_costantini@telespazio.it

The Recognition Problem

By means of the Hough Transform, each point in the imagecorresponds to a cone in parameter space, while each point inparameter space characterizes a circle in the image. Themapping is invertible.

Hough transform for circles

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Η→)sin()cos(

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Standard Hough transform presents different problems:– Computational complexity– Sensitivity to the differences between the shape in the image and the parametric curves used as

model for the detection

Hough transform drawbacks

Real Image Parameters space

Hough transform for straight lines

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