A New Method for Crater Detection Heather Dunlop November 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 χ 2 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 ● InsideRimOutsideWhole ● Compare regions with ● Euclidean distance or χ 2 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: /slides/svm_with_annotations.p df

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

Results

Conclusions ● Works better on day images than night ● The more training data the better ● Questions, comments, suggestions?