Fcv rep learned-miller

Distribution Fields

A Unifying Representation
for Low-Level Vision Problems
Erik Learned-Miller
with Laura Sevilla Lara, Manju Narayana,
Ben Mears

Computer Science Department

Unifying Low-Level Vision
 Tracking
 Optical Flow
 Affine invariant matching
 Stereo
 Backgrounding
 Registration
 Image Stitching
What kind of representation serves all these
problems well?

Distribution Fields 2

Unifying Descriptors and Representations

 HOG, SIFT, Shape Contexts
 Geometric blur
 Multi-scale methods
 Mixture of Gaussian backgrounding
 Bilateral filter
 Joint alignment (congealing)


Tracking


Basics of Tracking

Frame T Frame T+d


The Core Matching Problem
Find best match of patch I to image J,
for some set of transformations.
image J
patch I


Key issues
 Large “basin of attraction” in gradient descent
 Robustness to appearance changes of target


Local optimum problem in alignment
Stuck in a local
Unaligned
optimum


Common solution to gradient descent matching
 Blur images?
• “Spreads information”
• Also destroys information through averaging


Exploding an image

One plane
for each
feature
value.


Spatial Blur: 3d convolution with 2d Gaussian


Spatial Blur: 3d convolution with 2d Gaussian

KEY PROPERTY: doesn't destroy
information through averaging


Properties of Distribution Field Representation
 Much 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.


Properties of Distribution Field Representation
 Much 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!


The likelihood match


Sharpening match


Understanding the sharpening match

What standard deviation maximizes the likelihood of
a given point under a zero-mean Gaussian?


Intuition behind sharpening match
 Increase standard deviation until it matches
“average distance” to matching points.


Properties of the sharpening match
 A 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.


Basin of attraction studies



GIVEN A RANDOM PATCH...



AND A RANDOM DISPLACEMENT...


Basin of attraction results


Tracking results
 State of the art results on tracking with standard
sequences
• Very simple code
• Trivial motion model
• Simple memory model


Closely Related work
 Mixture of Gaussian backgrounding (Stauffer...)
 Shape contexts (Belongie and Malik)
 Congealing (me)
 Bilateral filter
 SIFT (Lowe), HOG (Dalal and Triggs)
 Geometric Blur (Berg)
 Rectified flow techniques (Efros, Mori)
 Mean-shift tracking
 Kernel tracking
 and many others...


Fcv rep learned-miller

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