Phase Scrambling for Image Matching in the Scrambled Domain

In recent years, signal matching has been required in many fields. A number of matching methods have been developed, and an appropriate method should be selected for each application in order to obtain the desired performance (1)(2). Phase-only correlation (POC), phase correlation or PHAse Transform (PHAT) (3)-(17), which is referred to herein as POC, is a phase-based correlation that is used for various applications, such as delay estimation (3)(4), motion estimation (5), registration (6)(7), video detection (8)(9), and biometrics authentication (10)(11). Phase-only correlation with Fourier transform was developed as PHAT in sound/sonar processing literature (3), and POCwith discrete Fourier transformwas proposed by Kuglin and Hines (12). The concept of POC is based on the fact that the information related to the displacement of two signals resides in the phase of the cross spectrum. Combining POC with various techniques, such as interpolation and curve fitting, provides highly accurate estimation (13)-(17). In special cases, the normalized cross spectrum corresponds to the product of the signs of discrete cosine transform (DCT) coefficients. Previously, we derived this relationship mathematically and proposed DCT sign phase correlation (DCT-SPC) based on this relationship (18). DCT-SPC is a phase-based correlation and has properties that are similar to those of POC. Images, particularly in the fields of biometrics, medicine, and surveillance camera require extreme security in order to avoid the risk of identity theft and invasion of privacy (19). Generally, encrypting and scrambling are used to protect information (20) (21). However, these protected images require decrypting or descrambling before image matching. In other words, neither POC nor DCT-SPC can be directly applied to conventional encrypted and scrambled images. Based on privacy concerns, secure multi-party techniques were applied to vision algorithms such as Blind Vision in (22). However, in (22), neither the registration nor the estimation of the geometric relationship between two images was discussed. In this chapter, for POC and DCT-SPC, we present phase-scrambled signals and a matching method that can be directly applied to phase-scrambled signals without descrambling. The presented methods are motivated by secure data management. The phase scrambling distorts only the phase information, which contains significant information of signals. Phase scrambling protects against the exposure of the information in the signal. Synchronized phase scrambling yields the relationship between non-scrambled signals. Therefore, POC and DCTSPC can be directly applied to phase-scrambled signals. Moreover, the presented scrambling 2