Overlapped Rectangle Image Representation and Its Application to Exact Legendre Moments Computatio

Linear quadtree is a popular image representation method due to its convenient imaging procedure. However, the excessive emphasis on the symmetry of segmentation, i.e. dividing repeatedly a square into four equal sub-squares, makes linear quadtree not an optimal representation. In this paper, a no-loss image representation, referred to as Overlapped Rectangle Image Representation (ORIR), is presented to support fast image operations such as Legendre moments computation. The ORIR doesn’t importune the symmetry of segmentation, and it is capable of representing, by using an identical rectangle, the information of the pixels which are not even adjacent to each other in the sense of 4-neighbor and 8-neighbor. Hence, compared with the linear quadtree, the ORIR significantly reduces the number of rectangles required to represent an image. Based on the ORIR, an algorithm for exact Legendre moments computation is presented. The theoretical analysis and the experimental results show that the ORIR-based algorithm for exact Legendre moments computation is faster than the conventional exact algorithms.

Rotation Scaling and Translation Invariants of 3D Radial Shifted Legendre Moments

This paper proposes a new set of 3D rotation scaling and translation invariants of 3D radially shifted Legendre moments. We aim to develop two kinds of transformed shifted Legendre moments： a 3D substituted radial shifted Legendre moments （3DSRSLMs） and a 3D weighted radial one （3DWRSLMs）. Both are centered on two types of polynomials. In the first case, a new 3D ra- dial complex moment is proposed. In the second case, new 3D substituted/weighted radial shifted Legendremoments （3DSRSLMs/3DWRSLMs） are introduced using a spherical representation of volumetric image. 3D invariants as derived from the sug- gested 3D radial shifted Legendre moments will appear in the third case. To confirm the proposed approach, we have resolved three is- sues. To confirm the proposed approach, we have resolved three issues： rotation, scaling and translation invariants. The result of experi- ments shows that the 3DSRSLMs and 3DWRSLMs have done better than the 3D radial complex moments with and without noise. Sim- ultaneously, the reconstruction converges rapidly to the original image using 3D radial 3DSRSLMs and 3DWRSLMs, and the test of 3D images are clearly recognized from a set of images that are available in Princeton shape benchmark （PSB） database for 3D image.

Orthogonal moment based texture segmentation

Texture segmentation is a necessary step to identify the surface or an object in an image. We present a Legendre moment based segmentation algorithm. The Legendre moments in small local windows of the image are computed first and a nonlinear transducer is used to map the moments to texture features and these features are used to construct feature vectors used as input data. Then an RBF neural network is used to perform segmentation. A k-mean algorithm is used to train the hidden layers of the RBF neural network. The training of the output layer is the supervised algorithm based on LMS. The algorithm has been successfully used to segment a number of gray level texture images. Compared with the geometric moment-based texture segmentation, we can reduce the error rates using orthogonal moments.