On Detection of Multiple Object Instances using Hough Transforms
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On Detection of Multiple Object Instances using Hough Transforms. Olga Barinova Moscow State University. Victor Lempitsky University of Oxford. Pushmeet Kohli Microsoft Research Cambridge. Hough transforms. Object detection → peaks identification in Hough images Beyond lines!!!

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On Detection of Multiple Object Instances using Hough Transforms

Olga Barinova

Moscow State University

Victor Lempitsky

University of Oxford

Pushmeet Kohli

Microsoft Research Cambridge


Hough transforms
Hough transforms Transforms

  • Object detection → peaks identification in Hough images

  • Beyond lines!!!

    • Ballard 1983 – Other primitives

    • Lowe, ICCV 1999 – Object detection

    • Leibe, Schiele BMVC 2003 – Object class detection

    • Last CVPR: Maji& Malik, Gall& Lempitsky, Gu et al. …


Category-level object detection Transforms

Example from Gall &Lempitsky CVPR 2009



Multiple lines detection
Multiple lines detection Transforms

  • Identifying the peaks in Hough images is highly nontrivial in case of multiple close objects

  • Postprocessing (e.g. non-maximum suppression) is usually used

  • Our framework is similar to Hough Transforms but doesn’t require finding local maxima and suppresses non-maxima automatically


Our framework

Elements space Transforms

Hough space

Our framework

Hypotheses

Voting elements


Our framework1

Elements space Transforms

Hough space

Our framework

1

2

3

x – labelling of voting elements,

xi = index of hypothesis,

if element votes for hypothesis,

xi = 0, if element votes for background

y – labelling of hypotheses, binary variables:

1 = object is present,

0 = otherwise


Our framework2

Elements space Transforms

Hough space

Our framework

x2=1

x3=1

x1=1

1

y1=1

y2=1

x4=2

2

y3=0

3

x8=2

x – labelling of voting elements,

xi = index of hypothesis,

if element votes for hypothesis,

xi = 0, if element votes for background

y – labelling of hypotheses, binary variables:

1 = object is present,

0 = otherwise

x6=2

x7=0

x5=2

Key idea : joint MAP-inference in x and y


Probabilistic derivation
Probabilistic derivation Transforms

Likelihood Term

  • Assume that given the existing objects y and the hypotheses assignmentsx, the distributions of the descriptors of voting elements are independent

  • Less crude than the independence assumption implicitly made by the traditional Hough

  • Prior Term

  • Occam razor (or MDL) prior penalizes the number of the active hypotheses


Probabilistic derivation1
Probabilistic derivation Transforms

voting elements

0

1

2

3

0

0

1

-∞ if xi = h, and yh = 0

0, otherwise

1

how likely is that voting element belongs to an object

Corresponds to the votes in standard Hough transform: Training stays the same!

2

3

0

0

1

“MDL” prior:

λ, if yh = 1

0, otherwise

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3

0

1

0

2

1

3

Problem known as facility location

hypotheses

0

[Delong et al. CVPR 2010] (today’s poster) looks at facility location with wider set of priors

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3


Probabilistic derivation2
Probabilistic derivation Transforms

0

voting elements

1

2

3

  • Tried different methods for MAP-inference

    • belief propagation

    • simulated annealing

  • They work well but don’t allow using large number of hypotheses

    • graph becomes huge and dense

    • sparsification heuristics required

0

0

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2

3

0

0

1

1

2

3

0

1

0

2

1

3

hypotheses

0

1

2

3


Probabilistic derivation3
Probabilistic derivation Transforms

0

voting elements

1

2

3

  • If labeling of y is given the values ofxiare independent

  • After maximizing out xwe get:

  • Large-clique, submodular

  • Greedy algorithm is as good as anything else (in terms of the approximation factor)

  • Greedy inference ~ iterative Hough voting

0

0

1

1

2

3

0

0

1

1

2

3

0

1

0

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hypotheses

0

1

2

3


Greedy maximization for our energy
Greedy maximization for our energy Transforms

Greedily add detections starting from the empty set

For each iteration

do the voting:

Seth0 = the overall maximum of HoughImage

IfHoughImage(h0) > λ, add h0 to detection set, else terminate

“standard” Hough vote for element i

Maximum over Hough votes for the hypotheses g that have already been switched on, including ‘background’

Sum over all voting elements


Inference
Inference Transforms

Using the Hough forest trained in [Gall&Lempitsky CVPR09]

Datasets from [Andriluka et al. CVPR 2008](with strongly occluded pedestrians added)


Results for pedestrians detection
Results for pedestrians detection Transforms

Hough transform

+ non-maximum suppression

Our framework

White = correct detection

Green = missing object

Red = false positive


Results for pedestrians detection1
Results for pedestrians detection Transforms

TUD-crossing

TUD-campus

Precision

Precision

Recall

Recall

Blue = Hough transform + non-maximum suppression

Light-blue = our framework


Results for lines detection
Results for lines detection Transforms

York Urban DB, Elder&Estrada ECCV 2008

  • our framework is able to discern very close yet distinct lines, and is in general much less plagued by spurious detections

Our framework

Hough + NMS


Conclusion
Conclusion Transforms

  • Framework for detecting multiple objects, greedy inference ~ iterated Hough transform

  • No need to find local maxima and suppress non-maxima – just take the only global maximum

  • Probabilistic model allows for extensions(ECCV paper coming: lines + vanishing points + horizon + zenith)

  • Training stays the same as for the recent Hough-based framework

  • Code available at the project page: http://graphics.cs.msu.ru/en/

    science/research/machinelearning/hough

Thank you for your attention!


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