Registration is one of the most common tasks of image analysis and computer vision applications. The requirements of most registration algorithms include large capture range and fast computation so that the algorithms are robust to different scenarios and can be computed in a reasonable amount of time. For these purposes, registration in the Fourier domain using normalized cross-correlation is well suited and has been extensively studied in the literature. Another common requirement is masking, which is necessary for applications where certain regions of the image that would adversely affect the registration result should be ignored. To address these requirements, we have derived a mathematical model that describes an exact form for embedding the masking step fully into the Fourier domain so that all steps of translation registration can be computed efficiently using Fast Fourier Transforms. We provide algorithms and implementation details that demonstrate the correctness of our derivations. We also demonstrate how this masked FFT registration approach can be applied to improve the Fourier-Mellin algorithm that calculates translation, rotation, and scale in the Fourier domain. We demonstrate the computational efficiency, advantages, and correctness of our algorithm on a number of images from real-world applications. Our framework enables fast, global, parameter-free registration of images with masked regions.

With the explosion in the usage of mobile devices and other smart electronics, embedded devices are becoming ubiquitous. Most such embedded architectures utilize fixed-point rather than floating-point computation to meet power, heat, and speed requirements leading to the need for integer-based processing algorithms. Operations involving Gaussian kernels are common to such algorithms, but the standard methods of constructing such kernels result in approximations and lack a property that enables efficient bitwise shift operations. To overcome these limitations, we present how to precisely combine the power of integer arithmetic and bitwise shifts with intrinsically real valued Gaussian kernels. We prove mathematically that there exist a set of what we call “magic sigmas” for which the integer kernels exactly represent the Gaussian function whose values are all powers-of-two, and we discovered that the maximum sigma that leads to such properties is about 0.85. We also designed a simple and precise algorithm for designing kernels composed exclusively of integers given any arbitrary sigma and show how this can be exploited for Gaussian filter design. Considering the ubiquity of Gaussian filtering and the need for integer computation for increasing numbers of embedded devices, this is an important result for both theoretical and practical purposes.

Registration is a ubiquitous task for image analysis applications. Generally, the requirements of registration algorithms include fast computation and large capture range. For these purposes, registration in the Fourier domain using normalized cross correlation is well suited and has been extensively studied in the literature. Another common requirement is masking, which is necessary for applications where certain regions of the image that would adversely affect the registration result should be ignored. To address these requirements, we have derived a mathematical model that describes an exact form for embedding the masking step fully into the Fourier domain. We also provide an extension of this masked registration approach from simple translation to also include rotation and scale. We demonstrate the computational efficiency of our algorithm and validate its correctness on several synthetic images and real ultrasound images. Our framework enables fast, global, parameter-free registration of images with masked regions.

Computer vision algorithms are seeing increased use in industrial inspection applications. Here, we present an "aid to visual" system that can detect post deformations of less than 0.005 inches in jet engine high pressure turbine disks. We create a gold-standard reference post from the posts of sample turbine disks and then use registration, edge detection, and curve-similarity algorithms to identify unacceptable post deformations. We address the challenges associated with adapting academic algorithms for use in functioning inspection systems. We present novel solutions to deal with practical issues such as accuracy, speed, robustness, and ease of use. Finally, we have integrated our algorithms into the software used in the work-flow of plant-factory inspectors, who will be able to identify minute post deformations that were previously difficult to detect