Printing:Thisposteris48”wideby36”high.It’sdesignedtobeprintedonalargeformatprinter.
CustomizingtheContent:Theplaceholdersinthisformattedforyou.placeholderstoaddtext,orclickanicontoaddatable,chart,SmartArtgraphic,pictureormultimediafile.
Ttext,justclicktheBulletsbuttonontheHometab.
Ifyouneedmoreplaceholdersfortitles,contentofwhatyouneedanddragitintoplace.PowerPoint’sSmartGuideswillhelpyoualignitwitheverythingelse.
Wanttouseyourownpicturesinsteadofours?Noproblem!JustpictureMaintaintheproportionofpicturesasyouresizebydraggingacorner.
Applying Techniques in Supervised Deep Learning to Steering Angle Prediction in Autonomous Vehicles
Vinay Sriram, Petar Penkov, James Ye
PROBLEM DEFINITION
IMAGE PRE-PROCESSING
CONVOLUTIONAL NEURAL NETWORK MODEL
RESULTS FUTURE WORK
• [1]Eliminatetop-halfoftheimages,anddownsamplebyafactorof100.Thissizecapturesnecessaryinformationforpredictionandisoflowenoughdimensionalitytoallowtraininganetworktobecomputationallyfeasible.
• [2]Applyedge-detection:Constructanimage𝑋 basedonthresholdingandtheSobelkerneloperatoroninput𝑋’:
Define 𝑆), 𝑆+ =−1 0 1−2 0 2−1 0 1
∗ 𝑋′,1 2 10 0 0−1 −2 −1
∗ 𝑋′
• Thedevelopmentofeffectiveautonomousvehiclesisapopularapplicationofmachinelearningandcontrol.
• Wewishtosolvealearningproblempredictingsteeringangles 𝛼4…𝛼6 7 overthecourseofaroadsegmentfromUdacity’s low-resolutionimages 𝑋4 …𝑋6 7 whereeach𝑋8 isdefinedbya640×480×3 RGBtensor.
• Wepartitionthedrivingdatawitha70:30train-to-testratiosuchthatthetest-setcontainssignificantturning.
• Introducemoreclasslabelstobetterapproximateanglecontinuity(forthis,moredatamustbecollectedtoprovideasufficienttrainingvolumeforhigher-magnitudelabels).
• Introduceadditionalconv.layerstoreducethebiasofthemodel,andrunstochasticgradientdescent(onresourceswithmorecomputationalpower)foragreaternumberofepochsforbetterconvergenceatlocaloptima.
• Computecross-imagegradientsthatcandeterminedirectionsoffeaturechangetobetterpredictturnangles.Foreach(𝑖, 𝑗) intheoutputimage,set𝑋8B = 255 ifeither
ofthefollowingaretrue,andset𝑋8B = 0 otherwise.• Sobelgradientmagnitude 𝑆)(𝑖, 𝑗)D + 𝑆+(𝑖, 𝑗)D isabove
somecutoffthreshold(preservingonlytheedges).• Grayscalevalueofthepixel(𝑖, 𝑗) isabovesomecutoff
threshold(preservingonlywhiteornear-whitesectionsoftheimage).Together,lanecaptureisreasonable.
𝑋′ 𝑋
Wediscretizetheproblem:eachsteeringanglegetsaclasslabel𝑥 ∈ 1,101 ,whereeachlabelrepresentsarangeof~0.01rad.ForwardPropagation:𝑧 IJ4 = 𝑊(I)𝑎(I) and𝑎 IJ4 = 𝑓I(𝑧 I )with𝑎8
(4) = 𝑥8 andℎO,P = 𝑎(QJ4).Layer𝑙 hasactivationfunc.𝑓(I) .
MaxPooling
[ClassProbabilities]
[InputImage]
[SoftmaxLayer] [Fully-ConnectedLayer] [Conv.Layer- ReLuActivation]
REFERENCESCameron,Oliver.OpenSourcing223GBofDrivingData.Medium,5Oct.‘16.
Pomerleau,Dean.NeuralNetPerceptionforMobileRobotGuidance.(1993)
UnsupervisedFeatureLearningandDeepLearningTutorial.Stanford.Web.http://ufldl.stanford.edu/tutorial/supervised/MultiLayerNeuralNetworks
Cost[𝑚 examples]:𝐽 𝑊, 𝑏 = 46∑ 4
DℎO,P 𝑥8 − 𝑦8
D68X4
TrainingusestheBack-Propagation algorithmtooptimizethecostJ.Theupdateruleis:∆𝑊 I ∶= ∆𝑊 I + 𝛻O \ 𝐽
with𝑊 I = 𝑊 I − 𝛼 46∆𝑊 I .
𝛿 I = 𝑊 I 7𝛿 IJ4 𝑓′(𝑧 I )
𝛻O \ 𝐽 = 𝛿(IJ4) 𝑎 I 7
𝛿^I = 𝑢𝑝𝑠𝑎𝑚𝑝𝑙𝑒(𝑊 I 7𝛿^
IJ4 )𝑓′(𝑧^I )
𝛻Oc\ 𝐽 = ∑ 𝑎 I ∗ 𝑟𝑜𝑡(𝛿^
IJ4 )68X4
ForTypicalLayers:
ForConvolutionalLayers
• Fortrainingandtesting,weconsideredinparticularhighwaydriving.Theconv.neuralnetworkwaseffectiveatpredictingsteeringanglewithinreasonableerror.
• Sobelpre-filteringofimagesprovidedverymarginalbenefits(between0.001and0.007RMSEontestsets).
• RMSEoftheabovetestsegmentwas0.031(withoutSobelpreprocessing)and0.034(withpreprocessing).
