Title of presentation goes here

Distribution FieldsA Unifying Representationfor Low-Level Vision ProblemsErik Learned-Millerwith Laura Sevilla Lara, Manju Narayana, Ben Mears Computer Science Department#Distribution FieldsUnifying Low-Level VisionTrackingOptical FlowAffine invariant matchingStereoBackgroundingRegistrationImage StitchingWhat kind of representation serves all these problems well?#Distribution FieldsUnifying Descriptors and RepresentationsHOG, SIFT, Shape ContextsGeometric blurMulti-scale methodsMixture of Gaussian backgroundingBilateral filterJoint alignment (congealing)

#Distribution FieldsTracking

#Distribution FieldsBasics of Tracking

Frame TFrame T+d#Distribution FieldsBasics of Tracking

Frame TFrame T+d#Distribution FieldsBasics of Tracking

Frame TFrame T+d#Distribution FieldsBasics of Tracking

Frame TFrame T+d#Distribution FieldsThe Core Matching Problem

patch Iimage JFind best match of patch I to image J,for some set of transformations.#Distribution FieldsKey issuesLarge basin of attraction in gradient descentRobustness to appearance changes of target#Distribution FieldsLocal optimum problem in alignmentUnalignedStuck in a localoptimum#Distribution FieldsCommon solution to gradient descent matchingBlur images?Spreads informationAlso destroys information through averaging

#Distribution FieldsExploding an image

One plane for each feature value.#Distribution FieldsSpatial Blur: 3d convolution with 2d Gaussian

#Distribution FieldsSpatial Blur: 3d convolution with 2d Gaussian

KEY PROPERTY: doesn't destroy information through averaging #Distribution FieldsProperties of Distribution Field RepresentationMuch larger basin of attraction than other descriptors. A useful probability model from a single image.Inherently multi-scale.Extension and unification of many popular descriptors.State of the art performance from extremely simple algorithms.

#Distribution FieldsProperties of Distribution Field RepresentationMuch larger basin of attraction than other descriptors. A useful probability model from a single image.Inherently multi-scale.Extension and unification of many popular descriptors.State of the art performance with extremely simple algorithms.

THANKS!#Distribution FieldsThe likelihood match

#Distribution FieldsSharpening match

#Distribution FieldsUnderstanding the sharpening match

What standard deviation maximizes the likelihood ofa given point under a zero-mean Gaussian?#Distribution FieldsIntuition behind sharpening matchIncrease standard deviation until it matches average distance to matching points.

#Distribution FieldsProperties of the sharpening matchA patch has probability of 1.0 under its own distribution field.Probability of an image patch degrades gracefully as it is translated away from best position.Optimum sigma value gives a very intuitive notion of the quality of the image match.

#Distribution FieldsBasin of attraction studies

#Distribution FieldsBasin of attraction studies

GIVEN A RANDOM PATCH...#Distribution FieldsBasin of attraction studies

AND A RANDOM DISPLACEMENT...#Distribution FieldsBasin of attraction studies

#Distribution FieldsBasin of attraction studies

#Distribution Fields

Basin of attraction results#Distribution FieldsTracking resultsState of the art results on tracking with standard sequencesVery simple codeTrivial motion modelSimple memory model#Distribution FieldsClosely Related workMixture of Gaussian backgrounding (Stauffer...)Shape contexts (Belongie and Malik)Congealing (me)Bilateral filterSIFT (Lowe), HOG (Dalal and Triggs)Geometric Blur (Berg)Rectified flow techniques (Efros, Mori)Mean-shift trackingKernel trackingand many others...#Distribution Fields