A New Method for Crater Detection

Heather DunlopNovember 2, 2006

Introduction● Purpose:

– Detect as many craters as possible– With as high an accuracy as possible

System Overview● Compute probability of a boundary image● Use Hough Transform to detect circles as

candidate craters● Compute a set of features on each

candidate● Apply SVM classifier to identify craters vs.

non-craters

Boundary Image● Canny Sobel

Boundary

Probability of a Boundary● Natural image boundary detection

– Martin, Fowlkes, Malik, UC Berkeley● Brightness, texture gradients● Half-disc regions described by histograms

● Compare distributions with χ2 statistic● Combine cues to form probability of a

boundary image

r

(x,y)

Hough Transform● For lines:

– “There are an infinite number of potential lines that pass through any point, each at a different orientation. The purpose of the transform is to determine which of these theoretical lines pass through most features in an image.” -- wikipedia.org

● For circles:– Parameterize by circle center (x,y) and radius

r– Each edge point votes for possible circles by

incrementing bin in accumulator matrix– Circles with the most votes win

Detect Circles● Threshold boundary image and apply

Hough Transform

Region Features● Features that can distinguish crater from non-

crater regions● Shading● Intensity● Texture● Template● Boundary● Radius● Lighting: azimuth angle, angle of incidence

Shading Features● Mostly applicable to day images● Linear gradient due to directional lighting● Compute best fit linear gradient● Features:

– direction of gradient– strength of gradient– SSE to gradient

Crater Regions● Inside Rim Outside Whole

● Compare regions with ● Euclidean distance or • χ2 statistic

r

δ

Intensity Features● Mean intensity

● Histogram of intensities

Texture● MR8 Filter bank: Varma, Zisserman

– Edges– Bars– Spots

– Multiple orientations and scales● Convolve images with set of filters● Aggregate responses● Cluster with k-means to form textons

Texton Maps● Compute nearest texton for each image

pixel's response vector● Form texton map for image

Texture Features● Histogram of textons in region

Template Features● Mostly applicable to night images

● Crater sort of looks like this:

● Sum element-wise multiplication with image and normalize by size

Boundary Features● Sum probability of a boundary in rim

normalized by area of rim

Support Vector Machines● Linear SVM: linear separator that

maximizes the margin

● For non-linearly separable data:

http://www-kairo.csce.kyushu-u.ac.jp/~norikazu/research.en.html

http://www.cs.cmu.edu/~awm/10701/slides/svm_with_annotations.pdf

Crater vs. Non-Crater Classifier● Train an SVM classifier using features

extracted● Training data:

– ground truth craters– Hough detected circles that are not craters

● On test image, apply classifier to candidate craters to determine probability that each is a crater

Experiments● 8 day images, 8 night images● 820 craters, approx. 50 per image● Each crater 4 pixels or larger in radius

marked as ground truth● Looking for craters of minimum radius 5

pixels● Leave-out-one-image cross validation

Results: Day

Legend: False positive Detected true positive Ground truth for true positive Not detected

Results: Night

Legend: False positive Detected true positive Ground truth for true positive Not detected

False Detections

Legend: False positive Detected true positive Ground truth for true positive Not detected

Performance Metrics● Precision: fraction of detections that are

true positives rather than false positives● Recall: fraction of true positives that are

detected rather than missed

ResultsImage Precision Recall

1 0.8 0.332 0.68 0.583 0.94 0.224 0.86 0.265 0.2 0.356 0.82 0.227 1 0.388 0.6 0.419 0.72 0.37

10 1 0.4111 0.59 0.3412 0.73 0.3313 0.78 0.6214 0.89 0.7115 0.89 0.7316 0.9 0.79

DayNight

All 0.77 0.44

Conclusions● Works better on day images than night● The more training data the better

● Questions, comments, suggestions?