filters and other potions - lcsllcsl.mit.edu/ldr-workshop/slides/perona_ldr_mit_112213.pdf ·...
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Filters and other potionsP. Perona - Caltech
MIT - 21 November 2013
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? whatwhere
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Architectures
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Architecture 1
Image(s)
The vision black box
Ripe bananas
Marble torso
train
build
ing
Feature extraction: texture
stereo disparity color contrast motion flow
edgels ….
Surface shape, scene depth,
spatial relationships, 3D motion
Grouping: image regions
Perceptual organization: 2.5D sketch:
boundaries, junctions, foregrnd, bckgrnd
Recognition, surface properties
Image processing Regions and surfacesObjects, verbs, categories…
motor
cognition
[Marr ’82]
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features?
Le Corbusier, Villa Savoyehttp://flickr.com/photos/ikura/1398271367/
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edges
http://www.iit.edu/~stawraf/perspx.jpgLe Corbusier, Villa Savoye
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[Fukushima ‘80]
Architecture 2
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[DeValois ’85]
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Column
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Hypercolumn
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Dense sampling
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translation, rotation invariance
[LeCun et al. 1998]
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scale invariance
[Lowe 2004]
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[Hinton et al. ’12]
translation, rotation, scale invariance
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96 filters 6 orientations 2 center-surround 14 scale samples over 2.2 binary octaves
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Detection Performance
Caltech pedestrians: 1M frames, 250K hand-annotated
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Detection Performance
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Detection Performance
Dollar et al. ‘10Dollar et al. ‘08
Viola & Jones ‘01
Dalal-Triggs ‘05 *
Walk et al. ‘10
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filter technology
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Scale, orientation, elongation…. lots of CPU cycles
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how do we make computations efficient?
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Separability
[Adelson & Bergen, ’85]Cost = m x n Cost = m + n
R(i, j) =X
h=1:M,k=1:N
k(h, k)I(i� h, j � k) R(i, j) =X
h=1:M
X
k=1:N
k(h)k0(k)I(i� h, j � k)
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Separability and decomposition
[Adelson & Bergen, ’85]
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Steerability
[Freeman & Adelson, ’91]
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General decomposition
k(x, ✓) =DX
i=1
bi(✓)fi(x)
k(x, y) =DX
i=1
fi(x)gi(y)
k(x, y; ✓) =DX
i=1
bi(✓)fi(x)gi(y)
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Design?
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x
✓
=k(x; ✓)
D
bi(✓)
✓
x
�i,i
fi(x)
A = USV T
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ApproximationK(x, y; ✓) =
DX
i=1
bi(✓)fi(x, y)
K(x, y; ✓) ⇡RX
i=1
bi(✓)fi(x, y) R ⌧ D
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[Perona ’95]
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[Perona ’95]
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[Perona ’95]
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Tensor Factorization
k(x, y; ✓) =DX
i=1
bi(✓)fi(x)gi(y)
•Not a convex problem •Gradient descent
[Shy, Perona ’96]
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Including scale by resampling
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[Manduchi et al. ’98][cfr. Simoncelli et al]
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Exploiting Image Statistics
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original
upsampled
sampling the gradient
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[Dollar et al. 2013]
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Gradient histograms[Dollar et al. 2013]
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Power law feature scaling
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Power law feature scaling
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Individual images
[Dollar et al. 2013]
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Fast computations
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Fast computations
[Dollar et al. 2013]
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Performance
[Dollar et al. 2013]
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Conclusions• Filtering front-end
• Need fine sampling of scale, orientation, …
• Scalable, separable and steerable approximations
• Exploiting image statistics to extrapolate
• Fast and accurate detection