This chapter discusses the issue of rotational invariance of a texture analysis system: i.e. one desires that the outcome of the analysis is not aaected by the orientation of the input image. We argue that the orthogonal DWT (section 3.4) is very impractical for such an analysis due to its separable nature in 2 dimensions. We therefore employ the non-separable wavelet frames (section 3.3). We d...

Scene matching is used for image registration in many fields. There are usually translation and an arbitrary unknown rotation angle between reference and template images. The corresponding scene matching algorithm costs far more computing time than that with small rotation angle and translation. Conceptions of generalized vector image, gray-scale image rotation transformation, gray-scale image ...

Rotation invariance and translation invariance have great values in image recognition tasks. In this paper, we bring a new architecture in convolutional neural network (CNN) named cyclic convolutional layer to achieve rotation invariance in 2-D symbol recognition. We can also get the position and orientation of the 2-D symbol by the network to achieve detection purpose for multiple non-overlap ...

   Negative data handling has gained a remarkable importance in the literature of Data Envelopment Analysis (DEA) to address many real life problems. Various erstwhile applications, in this arena, referred relocation of the origin to a superior (RDM) or to an inferior (Translated Input Oriented BCC) neighboring point. In this paper, the conditions for Rotation Invariance of various Data Envelop...

We propose to apply our recently developed frame-based framework for group-invariant morphology to the problem of tensor field morphology. Group invariance (and particularly rotation invariance) have been, and are, motivated to be relevant for filtering tensor fields. This leads to the development of a rotation-invariant frame for tensors, which can be used to easily define rotation-invariant m...

Most two-dimensional methods for wavelet shrinkage are efficient for edge-preserving image denoising, but they suffer from poor rotation invariance. We address this problem by designing novel shrinkage rules that are derived from rotationally invariant nonlinear diffusion filters. The resulting Haar wavelet shrinkage methods are computationally inexpensive and they offer substantially improved ...

Classical discrete wavelet packet transforms are sensitive to changes in image orientation and translation. Therefore, it is hardly possible to extract rotation invariant features from images in the transform domain. This paper proposes several algorithms for invariant discrete wavelet decomposition to produce an invariant representation for an image. The procedure can be divided into several s...