clasificación de imájenes

Beyond Bags of Features: Spatial Pyramid

Matching for Recognizing Natural Scene Categories

Svetlana Lazebnik Cordelia Schmid Jean Ponce

September 19, 2011

Svetlana Lazebnik, Cordelia Schmid, Jean Ponce Beyond Bags of Features: Spatial Pyramid Matching for Recognizing Natural Scene Categories

Motivation

Consider the problem of recognizing the semantic category of

an image.

Classify a photograph as depicting a scene (forest, street,

oce, etc.)

Bag-of- features approach with global geometric

correspondence

Subdividing the image and computing histograms of local

features at increasingly ne resolutions


Histogram intersection

I

l = I(H

l

X

,H lY

)=Di=1

min

(H

l

X

(i) ,H lY

(i))


Pyramid match kernel

matches found at level l also includes all the matches found

l + 1 new matches found at level l : I l I l+1 for l = 0, .., L 1penalize matches found in larger cells:

1

2

Ll

k

L(X ,Y ) = I L +L1l=0

1

2

Ll(I

l I l+1)k

L(X ,Y ) = 12

L

I

0 +Ll=1

1

2

Ll+1 Il


Pyramid match kernel


Spatial Matching Scheme

m: feature type

X

m

: coordinates of features of type m

for L levels and M channels

K

L(X ,Y ) =Mm=1k

L(Xm

,Ym

)

Vector dimensionality: M

Ll=0

4

l = M 13

(4

L+1 1)However, these operations are ecient because the histogram

vectors are extremely sparse

The computational complexity of the kernel is linear in the

number of features


Mercer's kernel

According to Mercer's theorem, a kernel K is positive semi-denite

if and only if there exists a mapping such thatK (xi

, xj

) = (xi

), (xj

) , xi

, xj

Xwhere , denotes a scalar dot productIs an inner product in a suitable feature space

V (H) =

H

(1)m H(1) H(r) m H(r) 1, .., 1,

0, ...0 , ..., , 1, ..., 1, 0, ...0 rst bin last bin

p-dimensional binary vector, p = m rm: total number of points in the histogram


Feature Extraction

1

Weak features

Oriented to edge points

Points whose gradient magnitude in given direction exceeds a

minimum threshold

Extract edge points at two scales and eight orientations

M = 16 channels

2

Strong features

SIFT descriptor

Dense regular grid

16 16 pixel patches

Vocabulary sizes: M = 200, M = 400 (k-means )


Experiments

Three diverse datasets:

fteen scene categories

Caltech-101 [3]

Graz

Perform all processing in grayscale

All experiments are repeated ten times with dierent randomly

selected training and test images

The nal result is reported as the mean and standard deviation

of the results from the individual runs

Multi-class classication: Support vector machine

(SVM),trained using the one-versus-all rule


Scene Category Recognition


Scene Category Recognition

Spatial pyramid kernel and strong features with M = 200

Latent semantic analysis (pLSA): Dimensionality reduction of

the feature space from 200 to 60


Confusion table

Confusion occurs between the indoor classes (kitchen, bedroom, living room)


Retrieval from the scene category database.


Caltech-101

This database contains from 31 to 800 images per category

The most diverse object database


The Graz database

High intra-class variation

Two object classes, bikes (373 images) and persons (460

images)

Train detectors for persons and bikes on 100 positive and 100

negative images

Results for strong features:


Conclusions

This paper presents a method for recognizing scene categories

based on approximate global geometric correspondence

Ecient algorithm, the computational complexity of the kernel

is linear in the number of features

Does very well on global scene classication tasks

When a class is characterized by high geometric variability, it is

dicult to nd useful global features


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