A connectionist model along with its state dynamics is developed for detecting corner points in binary and gray images. For a given binary/gray image, each pixel in the image is assigned with some initial cornerity (our measurable quantity) which is a vector representing the direction and strength of the corner. These cornerities are then mapped onto a neural-network model which is essentially designed as a cooperative computational framework. The cornerity at each pixel is updated depending on the neighborhood information. After the network dynamics settles to stable state, the dominant points are obtained by finding out the local maxima in the cornerities. Theoretical investigations are made to ensure the stability and convergence of the network. It is found that the network is able to detect corner points even in the noisy images and for open object boundaries. The dynamics of the network is extended to accept the edge information from gray images also. The effectiveness of the model is experimentally demonstrated in synthetic and real-life binary and gray images.