Semantic Object Segmentation - Video Segmentation and Its Applications - page 72

3.4.1 pLSA and LDA

Sivic et al. [ 50 ] discovered the object classes from a set of unlabeled images and
segmented images into different object classes using pLSA and LDA. They modeled
an image as a bag of visual words and ignored any spatial relationships among
visual words. Suppose there are M images in the data set. Each image j has N j
visual words. Each visual word w ji is assigned one of the K object classes according
to its label z ji . Under pLSA, the joint probability P has the form

of the graphical model shown in Fig. 3.8 a. The conditional probability P

( { w ji },{ d j },{ z ji } )

( w ji | d j )

marginalizing over topics z ji is given by

K
k = 1 P ( z ji = k | d j ) P ( w ji | z ji = k ) .

P ( w ji | d j )= (3.9)

P )

is the probability of visual word w ji occurring in object class k and is the model
of object class k . Fitting the pLSA model involves determining P

( z ji = k | d j ) is the probability of object class k occurring in image d j . P ( w ji | z ji = k

( w ji | z ji ) and

P by maximizing the following objective function using the Expectation

Maximization (EM) algorithm:

( z ji = k | d j )

N j
i = 1 P ( w ji | d j ) .

M
j = 1

L = (3.10)

Images are segmented into objects with semantic meanings based on the labels z ji
of visual words.
pLSA is a generative model only for training images but not for new images.
This shortcoming has been addressed by LDA, whose graphical model is shown in
Fig. 3.8 b. Under LDA,

{ φ k }

are models of object classes and are discrete distribu-
tions over the codebook of visual words. They are generated from a Dirichlet prior
Dir

( φ k ; β ) given by β . Each image j has a multinomial distribution π j over K object

Fig. 3.8 Graphical models
of pLSA and LDA