A Novel Approach for Quaternion Algebra Based JSEG Color Texture Segmentation

In this work, a novel colour quantization approach has been applied to the JSEG colour texture segmentation using quaternion algebra. As a rule, the fundamental vectors of the colour space are derived by inverting the three RGB colour directions in the complex hyperplanes. In the proposed system, colour is represented as a quaternion because quaternion algebra provides a very intuitive means of working with homogeneous coordinates. This representation views a colour pixel as a point in the three-dimensional space. A novel quantization approach that makes use of projective geometry and level set methods has been produced as a consequence of the suggested model. The JSEG colour texture segmentation will use this technique. The new colour quantization approach utilises the binary quaternion moment preserving thresholding methodology, and is therefore a splintering clustering method. This method is used to segment the colour clusters found inside the RGB cube and the colour consistency throughout the spectrum and in the space are both considered. The results of the segmentation are compared with JSEG as well as with the most recent standard segmentation techniques. These comparisons show that the suggested quantization technique makes JSEG segmentation more robust

Multi-directional colour edge detector using linear quaternion system convolution

A new linear colour image filter based on linear quaternion systems (LQSs) is introduced. It detects horizontal, vertical, left- and right-diagonal edges with a single LQS convolution mask. The proposed filter is a canonic minimal filter of four LQS filters, each with different angles of rotation combined parallel wise. Different angles of rotation are a key features of the new filter such that horizontal, vertical, left, and right-diagonal LQS filter masks rotate pixels through angles π/2, 5π/2, 3π/2, and 7π/2, respectively. Although, the four LQS masks are combined parallel to make a single LQS mask but derived using four quaternion convolutions, one for each direction of edges, the LQS filter produces a result without the combination of results from four separate edge detectors. This methodology could be generalised to design more elaborate LQS filters to perform other geometric operations on colour image pixels. The proposed filter translates smoothly changing colours to different shades of grey and produces coloured edges in multiple directions, where there is a sudden change of colour in the original image. Another key idea of the proposed filter is that it is linear because it operates in homogeneous coordinates

Color Image Analysis by Quaternion-Type Moments

International audienceIn this paper, by using the quaternion algebra, the conventional complex-type moments (CTMs) for gray-scale images are generalized to color images as quaternion-type moments (QTMs) in a holistic manner. We first provide a general formula of QTMs from which we derive a set of quaternion-valued QTM invariants (QTMIs) to image rotation, scale and translation transformations by eliminating the influence of transformation parameters. An efficient computation algorithm is also proposed so as to reduce computational complexity. The performance of the proposed QTMs and QTMIs are evaluated considering several application frameworks ranging from color image reconstruction, face recognition to image registration. We show they achieve better performance than CTMs and CTM invariants (CTMIs). We also discuss the choice of the unit pure quaternion influence with the help of experiments. appears to be an optimal choice

Quaternion convolutional neural networks for heterogeneous image processing

International audienceConvolutional neural networks (CNN) have recently achieved state-of-the-art results in various applications. In the case of image recognition, an ideal model has to learn independently of the training data, both local dependencies between the three components (R,G,B) of a pixel, and the global relations describing edges or shapes, making it efficient with small or heterogeneous datasets. Quaternion-valued convo-lutional neural networks (QCNN) solved this problematic by introducing multidimensional algebra to CNN. This paper proposes to explore the fundamental reason of the success of QCNN over CNN, by investigating the impact of the Hamilton product on a color image reconstruction task performed from a gray-scale only training. By learning independently both internal and external relations and with less parameters than real valued convolutional encoder-decoder (CAE), quaternion convolutional encoder-decoders (QCAE) perfectly reconstructed unseen color images while CAE produced worst and gray-scale versions. Index Terms-Quaternion convolutional encoder-decoder, convolutional neural networks, heterogeneous image processin