Coarse-level object recognition using interlevel products of complex wavelets

This paper introduces the Interlevel Product (ILP) which is a transform based upon the Dual-Tree Complex Wavelet. Coefficients of the ILP have complex values whose magnitudes indicate the amplitude of multilevel features, and whose phases indicate the nature of these features (e.g. ridges vs. edges). In particular, the phases of ILP coefficients are approximately invariant to small shifts in the original images. We accordingly introduce this transform as a solution to coarse scale template matching, where alignment concerns between decimation of a target and decimation of a larger search image can be mitigated, and computational efficiency can be maintained. Furthermore, template matching with ILP coefficients can provide several intuitive "near-matches" that may be of interest in image retrieval applications. © 2005 IEEE.

Digital watermarking with complex wavelets

In this paper, we propose a watermarking algorithm in the complex wavelet domain. We then model watermarking as a communication process and show that the complex wavelet domain has relatively high capacity and is a potentially good domain for watermarking. Finally, a technique for registering geometrically distorted images, which is based on motion estimation in the wavelet domain, is described. The registration process can assist watermark detection in a watermarked image attacked by Stirmark, for example.

Complex wavelets and shift invariance

Recently we have developed a new form of discrete wavelet transform, which generates complex coefficients by using a dual tree of wavelet filters to obtain their real and imaginary parts. This introduces limited redundancy (2 m:1 for m-dimensional signals) and allows the transform to provide approximate shift invariance and directionally selective filters (properties lacking in the traditional wavelet transform) while preserving the usual properties of perfect reconstruction and computational efficiency with good well-balanced frequency responses. In this paper we analyse why the new transform can be designed to be shift invariant, and describe how to estimate the accuracy of this approximation and design suitable filters to achieve this.

Biologically-inspired object recognition system with features from complex wavelets

In this paper, a novel cortex-inspired feed-forward hierarchical object recognition system based on complex wavelets is proposed and tested. Complex wavelets contain three key properties for object representation: shift invariance, which enables the extraction of stable local features; good directional selectivity, which simplifies the determination of image orientations; and limited redundancy, which allows for efficient signal analysis using the multi-resolution decomposition offered by complex wavelets. In this paper, we propose a complete cortex-inspired object recognition system based on complex wavelets. We find that the implementation of the HMAX model for object recognition in [1, 2] is rather over-complete and includes too much redundant information and processing. We have optimized the structure of the model to make it more efficient. Specifically, we have used the Caltech 5 standard dataset to compare with Serre's model in [2] (which employs Gabor filter bands). Results demonstrate that the complex wavelet model achieves a speed improvement of about 4 times over the Serre model and gives comparable recognition performance. © 2011 IEEE.

Robust pairwise matching of interest points with complex wavelets

We present a matching framework to find robust correspondences between image features by considering the spatial information between them. To achieve this, we define spatial constraints on the relative orientation and change in scale between pairs of features. A pairwise similarity score, which measures the similarity of features based on these spatial constraints, is considered. The pairwise similarity scores for all pairs of candidate correspondences are then accumulated in a 2-D similarity space. Robust correspondences can be found by searching for clusters in the similarity space, since actual correspondences are expected to form clusters that satisfy similar spatial constraints in this space. As it is difficult to achieve reliable and consistent estimates of scale and orientation, an additional contribution is that these parameters do not need to be determined at the interest point detection stage, which differs from conventional methods. Polar matching of dual-tree complex wavelet transform features is used, since it fits naturally into the framework with the defined spatial constraints. Our tests show that the proposed framework is capable of producing robust correspondences with higher correspondence ratios and reasonable computational efficiency, compared to other well-known algorithms. © 1992-2012 IEEE.