In conventional RBF network, the activation functions of hidden layers generally are symmetric functions like gaussian function. This has been considered to be one of the limiting factors for the network to speed up learning of accurately describing a given function. To avoid this criticism, a pseudo gaussian function whose deviation is changed according to the direction of incoming input is proposed. This property helps to estimate the given function more effectively with a minimal number of centers because of its flexibility of functional representation. A level set method is used to describe the asymmetric deviation of the pseudo gaussian function. To demonstrate the performance of the proposed network, a series of simulations are conducted for such cases as approximation of continuous functions and the time series estimation problem. From the simulation results, it can be concluded that the proposed pseudo gaussian function network shows excellent approximation accuracy and fast convergence.
In addition to basic simulation problems, image segmentation algorithm for X ray image is considerer for application of proposed neural network. The X ray image has the inherent properties of vagueness and blur in the boundary region and thus, it is difficult to detect edge or segment object region by conventional image processing algorithm. However, few approaches have been applied to X ray image segmentation because of blur of the X ray image and vagueness of its edge, which are inherent properties of X ray images. In the conventional active contour models, an edge-detector has been used to stop the evolving curve representing the boundary of the desired object. In the case of X ray image, detecting the edge with these methods is considered to be rather difficult due to blur of the X ray image and vagueness of its edge. To overcome this weak point, Mumford-Shah functional is used. Mumford-Shah model is an edge finding algorithm which does not based on the gradient of the image. The learning rule is derived form Mumford-Shah energy function and the boundary of segmented image is represented by neural network. To show the performance of the proposed method, some industrial problems of segmentation are solved. From the simulation results, proposed algorithm guarantees robust results even when various noises are added in the image.
RBF(Radial Basis Function Network)는 자주 쓰이는 간단한 구조의 신경회로망인데, 이 신경회로망의 활성화 함수는 가우시안 함수와 같은 대칭형의 함수를 사용한다. 이러한 성질은 신경회로망의 성능을 개선하는데 장애가 되어 왔는데 본 논문에서는 기존의 가우시안 함수를 기반으로 하여 입력에 따라 분산이 달라지는 함수를 새롭게 정의하고 이를 의사 가우시안 함수로 정의하고 이를 바탕으로 새로운 신경회로망을 구성하였다. 이 의사 가우시안 함수는 기존의 RBF 보다 성능이 개선되었으며 교사학습뿐 아니라 비교사 학습에도 좋은 성능을 보이는 것을 실험을 통해 보였다. 이 신경망을 영상처리의 문제중 이미지 세그먼테이션에 적용하였다. 이미지 세그먼테이션에 적용하는 학습룰을 Mumford-Shah 모델에 기반하여 제안하였으며 모의실험을 통해서 X ray 영상과 같이 경계가 불분명한 영상에 적용하여 기존의 active contour 모델에 비해서 개선된 성능을 보이는 것을 확인하였다.
