Crater Detection via Convolutional Neural Networks

1 MB·

by  Joseph Paul Cohen

Crater Detection via Convolutional Neural Networks
JosephPaulCohen, HenryZ.Lo, TingtingLu, andWeiDingattheUniversityofMassachusettsBoston({joecohen,
henryzlo,ding}@cs.umb.edu,[email protected])
Input Image
Introduction Convolutional Activations
Cratersareamongthemoststudiedgeomorphicfeatures
in the Solar System because they yield important
information about the past and present geological
processesandprovideinformationabouttherelativeages
of observed geologic formations. We present a method
for automatic crater detection using advanced machine
66 104 100 -2 -1 -2
learningtodealwiththelargeamountofsatelliteimagery
collected. 105 110 255 0 0 0 315
6 The challenge of automatically detecting craters 160 201 115 2 1 2 Output
1 comesfromtheiriscomplexsurfacebecausetheirshape
3x3 3x3
0
erodesovertimetoblendintothesurface. Bandeira[1] Input Window Convolutional Filter
2
providedaseminaldatasetthatembodiedthischallenge

n that is still an unsolved pattern recognition problem to Figure1: Convolutionallayer
a
this day. There has been work to solve this challenge
J
basedonextractingshape[2]andcontrast[1,3]features layers have an input which is a vector x of the previous
5
andthenapplyingclassificationmodelsonthosefeatures. layers outputs. These layers contain many nonlinear

] Thelimitingfactorinthisexistingworkistheuseof units. A nonlinear unit is a transformation h (x) which
V θ
handcraftedfiltersontheimagesuchasGabororSobel produces a single value where θ is a vector of weights.
C filters or Haar features. These hand crafted methods The most modern practice is to use a rectified linear
. rely on domain knowledge to construct. We would unit(ReLU):h (x) = max(0,(cid:80) θ x ). Theθ value
s θ i=0 i i
c like to learn the optimal filters and features based on at this layer will be altered during training in order to
[
training examples. In order to dynamically learn filters minimizeclassificationerror.

1 andfeatureswelooktoConvolutionalNeuralNetworks 4x4 Filter
v (CNNs)whichhaveshowntheirdominanceincomputer
8 vision [4]. The power of CNNs is that they can learn 4x4 Filter
. . . 7 image filters which generate features for high accuracy
9
classification.
0
......... 1.0 theCinNpuNtsimaraegoerghaansizceodmapsutaatcioonmsppuetarftioornmegdrapohn withaenrde ...
. . . 0 produce an output, then this output has computations 2 O(uetp) uts
6 performedonit,andthisisrepeateduntilanoutputlayer (c) Convolutional
1 whichcontainsaprediction.Therearemanycomponents (a) Input Image Layers (x20)
. . . v: tothesenetworksbutthemostsignificantparttodiscuss (15x15) (b) Convolutional (d)
i istheconvolutionallayerandthefullyconnectedlayer. Layers (x20) 500 Outputs
X Figure 2: Crater Convolutional Neural Network (CNN)
First we talk about a convolutional layer because
r architecturecomputation graph. Each layerisidentified
a this is the interface between the input image and the
withaletterandlinesshowprocessingfromlefttoright.
network. In Figure 1 the process of a convolutional
layer is shown. A sliding window is ran across the We combine the convolutional layers with fully
inputimagewithaconvolutionappliedateachposition. connected layers in a specific configration that has
Each pixel is multiplied by the corresponding filter achievedgoodperformanceoncraterdetectioninFigure
value and summed together which results in a single 2. Layer (a) is a 15x15 input image. Each candidate
value. A picture is formed from the results of these example is scaled to this size. Layers (b) and (c) are
convolutions. This design is important because spatial convolutional layers with 20 filters each of size 4x4.
informationismaintainedtobeusedlaterinthenetwork. Each filter is passed over the filter in a sliding window
In this example the filter values appear to be a sobel fashionwithastrideof1pixel. Unlikesimilarnetworks
filter however the filters learned will be much different. wedon’tuseapoolinglayerasitachievedpoorresults.
Duringthelearningprocessthevaluesofthefilterswill Layer(d)isafullyconnectedlayerwhereeachelement
be altered to minimize classification error of the entire of this layer is the result of h (x) with unique θs for
θ
network. each element. Layer (e) has just two outputs; each
Next we talk about a fully connected layer. These corresponding to a class. A softmax regression is used
2
Region U r b a c h ‘ 0B9 a n d eira ‘D1i0n g ‘ 1 1 C N N
West(1 24+1 25) 67.89 85.33 83.98 88.78
Center(2 24+2 25) 69.62 79.35 83.02 88.81
East(3 24+3 25) 79.77 86.09 89.51 90.29
Figure3:Acraterandnon-cratercandidateareprocessed Table1: F1-scorevia10-foldcrossvalidation.
by the first convolutional layer. Eight filters with
interesting activation patterns are shown to the right of
each candidate image in false color. Values are scaled
and then colored to make these values visible and to
maximize contrast within each square with blue = low
andred=high.
West1 24 Center2 24 East3 24
so that the results can be interpreted as a probability
distributionbetweencratersandnon-craters.
The filter and θ values throughout the network are
initialized randomly and incrementally modified using
stochastic gradient descent to minimize classification
error[4]. Thetermepochisatrainingcyclethatincludes
everytrainingexample. Weomitthediscussiononhow
West1 25 Center2 25 East3 25
trainingworksforspace.
Wecanvisualizethefilterslearnedforcraterstogain
Figure4: Labelsofeachcraterdatasettile.
insightintowhatfeaturesareimportanttoclassification.
We visualize 8/20 filters for layer (b) on a crater and
non-crater image in Figure 3. The filters, although
as a testing set while the remainder is used as a trainng
crude, can be seen to show vertical edges as well as
setwiththeresultingF1-Scoreaveragedtogether.
segmentation. The filters are learned based on what is
Our results are shown in Table 1. The scores were
nessary to minimize classification error on the training
obtained from the respective papers with the exception
datasotheydonotdirectlyrelatetowhatacraterisbut
of “Urbach ’09” which was obtained from [1] where it
maybefocusingonwhatisnotacrater.
isusedasabaselinecomparison. OurCNNapproachis
Evaluation trainedfor500epochsduringeachfoldevaluation. Our
We use Banderia’s [1] dataset1 to evaluate and compare proposed CNN method obtains a higher score than all
existingmethods. Weconcludethatconvolutionalneural
our method. It originates from the nadir panchromatic
networks have a large potential to significantly change
imagery footprint h0905 0000 that was captured by the
thewaycraterdetectionisperformed. Webelievefurther
HRSCaboardtheMarsExpressspacecraft. Thisdataset
improvementstothedesignofthecomputationgraphcan
is composed of 6 tiles (1700x1700 pixels each) with
increaseperformancemuchhigher.
resolution 12.5m/pixel. A domain expert has labeled
3658 craters across all tiles. Banderia utilized Urbach References
and Stepinski’s [2] highlight and shadow algorithm to [1] L. Bandeira, W. Ding, and T. F. Stepinski, “Automatic
avoid brute force sliding window candidate generation Detection of Sub-km Craters Using Shape and Texture
and reduce the total number of candidates that must Information,” in Proceedings of the 41st Lunar and
PlanetaryScienceConference,Mar.2010.
be evaluated. This pre-processing step results in 2022
[2] E. R. Urbach and T. F. Stepinski, “Automatic detection
cratersand2888non-cratersacrossalltiles. Theresults
of sub-km craters in high resolution planetary images,”
ofthispre-processingiswhathasbeenusedinpriorwork
PlanetaryandSpaceScience,vol.57,no.7,2009.
andisusedinourevaluationaswell.
[3] W.Ding,T.F.Stepinski,Y.Mu,L.Bandeira,R.Ricardo,
Prior work has used the F1-Score and Y. Wu, Z. Lu, T. Cao, and X. Wu, “Sub-kilometer
cross-validation to evaluate their methods. The craterdiscoverywithboostingandtransferlearning,”ACM
F1-Score is the harmonic mean between precision and TransactionsonIntelligentSystemsandTechnology,vol.2,
recall: F1 = 2·precision·recall. 10-Foldcrossvalidation no.4,Jul.2011.
precision+recall
is a testing procedure where the dataset is randomly [4] A.Krizhevsky,I.Sutskever,andG.E.Hinton,“ImageNet
dividedinto10sectionsandtheneachsectionisselected ClassificationwithDeepConvolutionalNeuralNetworks,”
inAdvancesinNeuralInformationProcessingSystems25,
1http://kdl.cs.umb.edu/w/datasets/craters/ 2012.