Primitive Manifold And Its Application In Image Analysis

Image representation is the theoretical basis of image analysis, involving multiplefields and disciplines. It has broad applications and profoundly affects the development ofdigital image processing technology. Since image basis function plays a key role in imagerepresentation research, image basis becomes a hot spot of current study. Due to thecomplex geometric structure in image, a better image basis often has a large family withlots of basis functions. Therefore, the corresponding image transform and analysis wouldbe very resource intensive and time consuming.Manifold learning algorithms are developed for discovering intrinsic features inimages. In this paper, a novel image representation is proposed, called―primitivemanifold‖. One primitive manifold which is considered as a basic cell can represent all thebasis functions lying in the same manifold. In order to obtain the mathematicalrepresentation model of primitive manifold, an existing manifold learning algorithm isused with primitive image set for dimensionality reduction, and then the manifold isapproximated by Taylor expansion. On the basis of the model, a manifold distancemeasurement criteria based on the correlation of primitive manifold is proposed. Fastimage decomposition and reconstruction method based on primitive manifold is given. Itis pointed out that the advantage of the primitive manifold model in computingperformance by theoretical analysis and experimental verification. Furthermore, someimage basis functions are combined with primitive manifold model for realizing imagedenoising, edge detection and face recognition. It shows that the method has a wideapplication prospect.Experimental results show that, compared with traditional image representationmethods, primitive manifold based image analysis reduces time consumption, discoversthe latent intrinsic structure of images more efficiently and provides the possibility ofempirical prediction.