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Contour Grouping

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					    Qualifying Exam:


Contour Grouping
         Vida Movahedi


     Supervisor: James Elder
       Supervisory Committee:

  Minas Spetsakis, Jeff Edmonds


          York University
           Summer 2009
                         Contents
• Introduction

• Preliminary Concepts
   – Pre-processing
   – Gestalt cues

• Methods
   – Local & Heuristic
   – Local & Probabilistic
   – Global Saliency

• Evaluation

• Conclusion & open problems
                         Contents
• Introduction

• Preliminary Concepts
   – Pre-processing
   – Gestalt cues

• Methods
   – Local & Heuristic
   – Local & Probabilistic
   – Global Saliency

• Evaluation

• Conclusion & open problems
             Introduction
• Segmentation
 Partition an image into regions, each corresponding to
 an object or entity


• Figure-Ground segmentation
    Segmentation Methods
• Regional Segmentation
  – Use regional info, optimize labelling of regional tokens,
    e.g. clustering
  – Depending on uniformity in object region

• Active Contour Models
  – Use regional (external) & boundary (internal) info,
    optimize deformation of model
  – Sensitivity to initialization, too smooth


• Contour Grouping
  – Use boundary info (& regional info), optimize grouping
    of contour fragments
           Problem Definition
• Input:      Color image

• Goal:       Figure-ground segmentation

• Method:     Contour Grouping

• Other available info: None
  - No motion, stereo or video information

  - No user interactions

  - No assumptions on object types, shapes, color, etc.

  - No assumptions on background or lighting conditions
                Challenges
• High-dimensional data space, lots of information,
  many cues
• Unknown cue integration
• Global optimization in a non-convex
  multidimensional space
• Camera, imaging, quantization noise
• Clutter in natural scenes
• Occluded or overlapping objects
                         Contents
• Introduction

• Preliminary Concepts
   – Pre-processing
   – Gestalt cues

• Methods
   – Local & Heuristic
   – Local & Probabilistic
   – Global Saliency

• Evaluation

• Conclusion & open problems
                             Steps
                               Pre-processing
    Image

                  Edge                      Line /Curve
                Detection                  Approximation




                                                           Figure/Ground
                            Grouping Algorithm
                                                            Segmentation
                  Saliency                 Optimization
  Learned       Computations                 Algorithm
Parameters or
Distributions
        Pre-processing




Image Edge Map  Line Map  Contour
               Gestalt Cues
How is grouping done in human vision?

• Proximity
• Similarity
   – Brightness
   – Contrast

• Good continuation
   – Parallelism
   – Co-circularity
                         Contents
• Introduction

• Preliminary Concepts
   – Pre-processing
   – Gestalt cues

• Methods
   – Local & Heuristic
   – Local & Probabilistic
   – Global Saliency

• Evaluation

• Conclusion & open problems
        Grouping Methods
• Local Heuristic methods
  – Defining a heuristic cost for contour
    hypotheses, find the optimal one

• Local Probabilistic methods
  – Find posterior probability of contour
    hypotheses given cues, find the optimal one

• Global methods
  – An extra step of calculating global saliencies
    based on local measures
                         Contents
• Introduction

• Preliminary Concepts
   – Pre-processing
   – Gestalt cues

• Methods
   – Local & Heuristic
   – Local & Probabilistic
   – Global Saliency

• Evaluation

• Conclusion & open problems
          Local & Heuristic
     Example: Ratio Contour Method
              (Wang et. al, PAMI’05)




• Detected/ virtual fragments

• Contour cost= curvature & gap per unit length

• Graph model

• Alternate cycle
                        Local & Heuristic
          Example: Ratio Contour Method
                                      (Wang et. al, PAMI’05)
• Edge/ Link costs
    w(e)         [ (t )  
                                  2
                                      (t )]dt
                B (e)
                                                               (C ) 
                                                                       
                                                                       eC
                                                                             w(e)
     (t )  
                1 if v(t ) is on a virtual fragment
                0 if v(t ) is on a real fragment
                                                                       
                                                                       eC
                                                                             l ( e)

     l ( e)      dt
                B (e)



• Ratio Contour Algorithm
 Sample Results for RC method
                              Image           RC               RRC
         Image




           RC




(from Wang et al., PAMI’05)

                                 (from Stahl & Wang, TIP’07)
                         Contents
• Introduction

• Preliminary Concepts
   – Pre-processing
   – Gestalt cues

• Methods
   – Local & Heuristic
   – Local & Probabilistic
   – Global Saliency

• Evaluation

• Conclusion & open problems
                Local & Probabilistic
                               (Elder et al., PAMI’03)


• Bayesian Rule:
                 p ( D | H ). p ( H )        1                    p( D | H )       p( H )
     p( H | D)                                           L                ,P 
                                        1  LP                 p( D | H )      p(H )
                                                 1
                        p( D)

• Contour saliency= posterior probability of contour
  c  (t1 ,..., t n 1 )  C ,  i  {1... N }, i  {1...n}

  c*  arg max p(c  C | D)
                c



• Assumptions:
   – Markov Chain Assumption
   – Independence of evidence from cues                                   p(c  C | D)   pio        p            c
                                                                                                                    ij
                                                                                                              
                                                                                            ti c   ( ti ,t j )c
   – Comparing contours of same length
                 Local & Probabilistic
                               (Elder et al., PAMI’03)

• Graph Model
                                                                                   
    log  p (c  C | D)    log( p )   log( p )  
                                  o               c      wo (vi )   wc (eij ) 
                               
                                  i               ij
                                                       v P
                                                                                  
                            ti c       ( ti ,t j )c  i c          ( vi ,v j )Pc 

• Node weight
  wo (vi )   log( pio ), i  1.. N                                         vi     eij   vj

• Link weight
    wc (eij )   log( pij ), i, j  1..N
                        c




• Shortest path/cycle
• Approximate search
Sample Results for Probabilistic Methods




             (from Estrada & Elder- CVPRW’06)
                         Contents
• Introduction

• Preliminary Concepts
   – Pre-processing
   – Gestalt cues

• Methods
   – Local & Heuristic
   – Local & Probabilistic
   – Global Saliency

• Evaluation

• Conclusion & open problems
         Global Model

Local weights      Global weights
               Global Saliency
• Edge/Link Affinity
    Based on collinearity, proximity, etc.

• Edge/ Link Saliency
    Relative number of closed random
    walks which visit that edge/link
    (Mahamud et al., PAMI’03)

• Shown to be relevant to the
  eigenvalues and eigenvectors of
  the affinity matrix

• Grouping based on global saliency
Some Results of the Untangling method




          (from Zhu; Song; Shi- ICCV’07)
                         Contents
• Introduction

• Preliminary Concepts
   – Pre-processing
   – Gestalt cues

• Methods
   – Local & Heuristic
   – Local & Probabilistic
   – Global Saliency

• Evaluation

• Conclusion & open problems
              Evaluation
• Empirical discrepancy methods
  The output of algorithms is compared with a
  reference segmentation or ground truth



• Requirements
  – A ground truth dataset
  – An error measure
SOD: Salient Object Dataset
• Based on Berkeley Segmentation Dataset (BSD)

• 300 images, randomly showing 818
  segmentations (half of BSD) to each of 7 subjects

• 12,110 object boundaries obtained
                                   1
                               1




                           1

                       1


                                   1
 Region-based Error Measures
• Example


                     RA  RB
 RIM ( A, B)  1 
                     RA  RB
                 | RA |  RA  RB       | RB |  RA  RB
                                   
                     RA  RB                RA  RB


• Not sensitive to some large shape features
  (e.g., spikes, wiggles)
            Boundary-based Error
                 Measures
d B (a)  min d (a, b) , a  A
          bB

SDB ( A, B)  {d B (a), a  A}


h( A, B)  max(SDB ( A, B))  max min d (a, b)
                                    aA   bB
H ( A, B)  max h( A, B), h( B, A) 


• Not sensitive to object topology and some
  large shape features (e.g., loop-backs,
  wiggles)
         Mixed Error Measures
• Example

              1 1                                          
                         N fn               N fp
                                      1
  MM ( A, B)  
              2  N fn
                         dA( pj )  N          d B ( qk ) 
                                                            
                        j 1          fp   k 1            

   pj, j=1..Nfn are pixels in the
   false negative region (RB-RA)
   qk, k=1..Nfp are pixels in the
   false positive region (RA-RB)

• Not sensitive to some large shape features. Does
  not respect ordering along contours.
  Contour Mapping Measure
• Based upon a matching between
  all points on the two boundaries

• Monotonically non-decreasing

• Allowing one-to-one, many-to-
  one, and one-to-many matching      Contour Mapping Distance=7.73




• Error= average distance between
  matched pairs

• Dynamic Programming
                         Contents
• Introduction

• Preliminary Concepts
   – Pre-processing
   – Gestalt cues

• Methods
   – Local & Heuristic
   – Local & Probabilistic
   – Global Saliency

• Evaluation

• Conclusion & open problems
Conclusion & Open Problems
• Cue selection and combination

• Grouping Model
   –   Global saliency
   –   Probabilistic models

• Optimization Algorithms

• Hierarchical and multi-scale algorithms

• Quantitative evaluation

				
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