16. The method according to claim 15 , in which the number of concepts, K, is choosen to maximize log ⁡ ( P ⁡ ( F , V ) ) - m K 2 ⁢ log ⁡ ( MN ) where m K is the number of free parameters needed for a model with K mixture components; and m K =(K−1)+K(M−1)+K(N−1)+L 2 =K(M+N−1)+L 2 −1.
16. The method according to claim 15 , in which the number of concepts, K, is choosen to maximize log ⁡ ( P ⁡ ( F , V ) ) - m K 2 ⁢ log ⁡ ( MN ) where m K is the number of free parameters needed for a model with K mixture components; and m K =(K−1)+K(M−1)+K(N−1)+L 2 =K(M+N−1)+L 2 −1. 17. The method according to claim 16 , wherein a joint distribution is used to model the probability of an event that a word w 3 belonging to semantic concept z k is an annotation word of image ƒ i : P ⁡ ( w j , z k , f i ) = P z ⁡ ( Z k ) ⁢ p ⁡ ( f i ❘ z k ) ⁢ P V ⁡ ( w j ❘ z k ) P ⁡ ( w j ❘ f i ) = ∫ P v ⁡ ( w j ❘ z ) ⁢ p ⁡ ( z ❘ f i ) ⁢ ⅆ z = ∫ P V ⁡ ( w j ❘ z ) ⁢ p ⁡ ( f i ❘ z ) ⁢ P ⁡ ( z ) p ⁡ ( f i ) ⁢ ⅆ z = E z ⁢ { P v ⁡ ( w j ❘ z ) ⁢ p ⁡ ( f i ❘ z ) p ⁡ ( f i ) } or where 
 p (ƒ i )=∫p ℑ (ƒ i |z ) P z ( z ) dz=E z {p ℑ (ƒ i |z )}, and E z {•} denotes the expectation over P(z k ); and a Monte Carlo integration is used to derive P ⁡ ( w j ❘ f i ) ≈ ∑ k = 1 K ⁢ P V ⁡ ( w j ❘ z k ) ⁢ p ⁡ ( f i ❘ z k ) ∑ h = 1 K ⁢ p ⁡ ( f i ❘ z h ) ⁢ ⁢ ⁢ = ∑ k = 1 K ⁢ P V ⁡ ( w j ❘ z k ) ⁢ x k ⁢ where ⁢ ⁢ x k = p ⁡ ( f i ❘ z k ) ∑ h = 1 K ⁢ p ⁡ ( f i ❘ z h ) , and wherein the words with the top highest P(w j |ƒ i ) are returned to annotate the image.