Monotonic sequences for image enhancement and segmentation

Both image enhancement and image segmentation are important pre-processing steps for various image processing fields including autonomous navigation, remote sensing, computer vision, and biomedical image analysis. Both methods have their merits and their short comings. It then becomes obvious to ask the question: is it possible to develop a new better image enhancement method which has the key elements from both segmentation and image enhancement techniques? The choice of the threshold level is a key task in image segmentation. There are other challenges of image segmentation. For example, it is very difficult to perform the image segmentation in poor data such as shadows and noise. Recently, a homothetic curves Fibonacci-based cross sections thresholding has been developed for the de-noising purposes. Is it possible to develop a new image cross sections thresholding method, which can be used for both segmentation and image enhancement purposes? This paper a) describes a unified approach for signal thresholding, b) extends cross sections concept by generating and using a new class of monotonic, piecewise linear, sequences (slowly or faster growing than Fibonacci numbers) of numbers; c) uses the extended sections concept to the image enhancement and segmentation applications. Extensive experimental evaluation demonstrates that the newly proposed monotonic sequences have great potential in image processing applications, including image segmentation and image enhancement applications. Moreover, study has shown that the generalized cross techniques are invariant under morphological transformations such as erosion, dilation, and median, able to be described analytically, can be implemented by using the look up table methods.