Di Zang

Signal modeling for two-dimensional image structures

This paper presents a novel approach towards two-dimensional (2D) image structures modeling. To obtain more degrees of freedom, a 2D image signal is embedded into a certain geometric algebra. Coupling methods of differential geometry, tensor algebra, monogenic signal and quadrature filter, a general model for 2D image structures can be obtained as the monogenic extension of a curvature tensor. Based on this model, local representations for the intrinsically one-dimensional (i1D) and intrinsically two-dimensional (i2D) image structures are derived as the monogenic signal and the generalized monogenic curvature signal. From the local representation, independent features of local amplitude, phase and orientation are simultaneously extracted. Compared with the other related work, the remarkable advantage of our approach lies in the rotationally invariant phase evaluation of 2D structures, which delivers access to phase-based processing in many computer vision tasks.

Dense optical flow estimation from the monogenic curvature tensor

In this paper, we address the topic of estimating two-frame dense optical flow from the monogenic curvature tensor. The monogenic curvature tensor is a novel image model, from which local phases of image structures can be obtained in a multi-scale way. We adapt the combined local and global (CLG) optical flow estimation approach to our framework. In this way, the intensity constraint equation is replaced by the local phase vector information. Optical flow estimation under the illumination change is investigated in detail. Experimental results demonstrate that our approach gives accurate estimation and is robust against noise contamination. Compared with the intensity based approach, the proposed method shows much better performance in estimating flow fields under brightness variations.

The monogenic curvature scale-space

In this paper, we address the topic of monogenic curvature scale-space. Combining methods of tensor algebra, monogenic signal and quadrature filter, the monogenic curvature signal, as a novel model for intrinsically two-dimensional (i2D) structures, is derived in an algebraically extended framework. It is unified with a scale concept by employing damped spherical harmonics as basis functions. This results in a monogenic curvature scale-space. Local amplitude, phase and orientation, as independent local features, are extracted. In contrast to the Gaussian curvature scale-space, our approach has the advantage of simultaneous estimation of local phase and orientation. The main contribution is the rotationally invariant phase estimation in the scale-space, which delivers access to various phase-based applications in computer vision.

Detecting intrinsically two-dimensional image structures using local phase

This paper presents a novel approach towards detecting intrinsically two-dimensional (i2D) image structures using local phase information. The local phase of the i2D structure can be derived from a curvature tensor and its conjugate part in a rotation-invariant manner. By employing damped 2D spherical harmonics as basis functions, the local phase is unified with a scale concept. The i2D structures can be detected as points of stationary phases in this scale-space by means of the so call phase congruency. As a dimensionless quantity, phase congruency has the advantage of being invariant to illumination change. Experiments demonstrate that our approach outperforms Harris and Susan detectors under the illumination change and noise contamination.

Phase based image reconstruction in the monogenic scale space

In this paper, we present an approach for image reconstruction from local phase vectors in the monogenic scale space. The local phase vector contains not only the local phase but also the local orientation of the original signal, which enables the simultaneous estimation of the structural and geometric information. Consequently, the local phase vector preserves a lot of important information of the original signal. Image reconstruction from the local phase vectors can be easily and quickly implemented in the monogenic scale space by a coarse to fine way. Experimental results illustrate that an image can be accurately reconstructed based on the local phase vector. In contrast to the reconstruction from zero crossings, our approach is proved to be stable. Due to the local orientation adaptivity of the local phase vector, the presented approach gives a better result when compared with that of the Gabor phase based reconstruction.

Monogenic Curvature Tensor as Image Model

In this chapter, a new rotation-invariant generalization of the analytic signal will be presented to analyze intrinsic 1D and 2D local image structures. By combining differential geometry and Clifford analysis, the monogenic curvature tensor can be derived to perform a split of identity and to enable simultaneous estimation of local amplitude, phase, main orientation, and angle of intersection in a monogenic scale-space framework.