Invariant image classification using triple-correlation-basedneural networks

Triple-correlation-based neural networks are introduced and used in this paper for invariant classification of 2D gray scale images. Third-order correlations of an image are appropriately clustered, in spatial or spectral domain, to generate an equivalent image representation that is invariant with respect to translation, rotation, and dilation. An efficient implementation scheme is also proposed, which is robust to distortions, insensitive to additive noise, and classifies the original image using adequate neural network architectures applied directly to 2D image representations. Third-order neural networks are shown to be a specific category of triple-correlation-based networks, applied either to binary or gray-scale images. A simulation study is given, which illustrates the theoretical developments, using synthetic and real image data.     

Two-dimensional filter bank design for optimal reconstruction usinglimited subband information

In this correspondence, we propose design techniques for analysis and synthesis filters of 2-D perfect reconstruction filter banks (PRFB's) that perform optimal reconstruction when a reduced number of subband signals is used. Based on the minimization of the squared error between the original signal and some low-resolution representation of it, the 2-D filters are optimally adjusted to the statistics of the input images so that most of the signal's energy is concentrated in the first few subband components. This property makes the optimal PRFB's efficient for image compression and pattern representations at lower resolutions for classification purposes. By extending recently introduced ideas from frequency domain principal component analysis to two dimensions, we present results for general 2-D discrete nonstationary and stationary second-order processes, showing that the optimal filters are nonseparable. Particular attention is paid to separable random fields, proving that only the first and last filters of the optimal PRFB are separable in this case. Simulation results that illustrate the theoretical achievements are presented.