The power of quantum mechanics has been extensively exploited to meet the high computational requirement of classical image processing. However, existing quantum image models can only represent the images sampled in Cartesian coordinates. In this paper, quantum log-polar image (QUALPI), a novel quantum image representation is proposed for the storage and processing of images sampled in log-polar coordinates. In QUALPI, all the pixels of a QUALPI are stored in a normalized superposition and can be operated on simultaneously. A QUALPI can be constructed from a classical image via a preparation whose complexity is approximately linear in the image size. Some common geometric transformations, such as symmetry transformation, rotation, etc., can be performed conveniently with QUALPI. Based on these geometric transformations, a fast rotation-invariant quantum image registration algorithm is designed for log-polar images. Performance comparison with classical brute-force image registration method reveals that our quantum algorithm can achieve a quartic speedup.

A novel quantum representation for log-polar images

Image registration is an essential step in many image processing applications that need visual information from multiple images for comparison, integration, or analysis. Recently, researchers have introduced image registration techniques using the log-polar transform (LPT) for its rotation and scale invariant properties. However, it suffers from nonuniform sampling which makes it not suitable for applications in which the registered images are altered or occluded. Inspired by LPT, this paper presents a new registration algorithm that addresses the problems of the conventional LPT while maintaining the robustness to scale and rotation. We introduce a novel adaptive polar transform (APT) technique that evenly and effectively samples the image in the Cartesian coordinates. Combining APT with an innovative projection transform along with a matching mechanism, the proposed method yields less computational load and more accurate registration than that of the conventional LPT. Translation between the registered images is recovered with the new search scheme using Gabor feature extraction to accelerate the localization procedure. Moreover an image comparison scheme is proposed for locating the area where the image pairs differ. Experiments on real images demonstrate the effectiveness and robustness of the proposed approach for registering images that are subjected to occlusion and alteration in addition to scale, rotation, and translation.

Image Registration Using Adaptive Polar Transform

Almost all computer vision applications, from remote sensing and cartography to medical imaging and biometrics, use image registration or alignment techniques that establish spatial correspondence (one-to-one mapping) between two or more images. These images depict either one planar (2-D) or volumetric (3-D) scene or several such scenes and can be taken at different times, from various viewpoints, and/or by multiple sensors. In medical image processing and analysis, the image registration is instrumental for clinical diagnosis and therapy planning, e.g., to follow disease progression and/or response to treatment, or integrate information from different sources/modalities to form more detailed descriptions of anatomical objects-of-interest. The unified registration goal – aligning a 2-D or 3-D target (sensed) image with a reference image – is reached by specifying a mathematical model of image transformations for and determining model parameters of the desired alignment. Frequently, the parameters provide an optimum of a goal function supported by the parameter space, so that the registration reduces to a certain optimization problem. This chapter overviews the 2-D and the 3-D medical image registration with special reference to the state-of-the-art robust techniques proposed for the last decade and discusses their advantages, drawbacks, and practical implementations.

State-of-the-Art Medical Image Registration Methodologies: A Survey

With the development of integrated circuit (IC) chips, many elongated chips with small amounts of textures have begun to be used in IC packaging and manufacturing. Traditional template-matching methods are not effective for positioning these chips; this limitation results in IC equipment that cannot accurately pick up an elongated IC chip or may package a nonworking IC chip onto an electronic device. In this paper, a novel region-based normalized cross correlation algorithm that uses a signal function to separate the influences of the IC chip and the background pixel information is proposed. To obtain an increased speed, the bounding box of the IC chip is employed to rapidly estimate the region of interest of an IC chip in a target image. Various experiments using LED sorting equipment demonstrate that our algorithm results in correct positioning for elongated IC chips and can distinguish good chips from nonworking chips with reasonable accuracy. When the size of the target image is 512 × 512 pixels and the size of the template image is smaller than 140 × 140 pixels, the matching time of our algorithm is less than 14 ms. This algorithm may have many applications in the field of IC packaging.

A Region-Based Normalized Cross Correlation Algorithm for the Vision-Based Positioning of Elongated IC Chips

Image registration is an essential task in many image processing applications. Log-polar transform (LPT) is a well known tool for image processing for its rotation and scale invariant properties. However it suffers from nonuniform sampling which makes it not suitable for the environment when registered images are altered or occluded. Inspired by LPT, this paper presents a new algorithm that addresses the problems of the conventional LPT while maintaining the invariant properties. We introduce adaptive polar transform (APT) technique and an innovative matching mechanism that serve as image processing tool for recovering scale and rotation change of the registered image. Unlike the conventional LPT that focuses only at the fovea area of the registered image, our proposed APT gives even consideration to the entire image. Translation of the registered image is recovered with the new search scheme by using Gabor feature extraction to accelerate the localization procedure. The experimental results indicate that our proposed method outperforms conventional LPT in registering images that are altered or occluded.

http://www2.ece.ohio-state.edu/~zheng/publications/Log-Polar-ITR-IMA.pdf

Image registration using Adaptive Polar Transform

Object recognition is an essential task in many image processing applications. Although object appears as three-dimensional in real world, they are usually perceived as two-dimensional in digital image or video. In most cases, major problems in recognizing objects lie on the two-dimensional geometry changes in object appearances. This paper presents an innovative template matching based object recognition method that is invariant to rotation and scale changes as well as resistant to noise. The approach is achieved by combining feature based search strategy and object matching in Log-Polar domain. Translation of the object is recovered with the new Gabor feature extraction method applied in the Cartesian coordinate. The multi-resolution Log-Polar search method is invented to reduce the number of feature point for Log-Polar matching in the target image. The new similarity measure for classification and verification is also proposed. The innovative combination of these techniques yields robustness in object recognition for fast computation without any rescaling in the target image. Comparisons of the repeatability factor of the new Gabor feature extraction with other well-known techniques such as SIFT and Harris-Laplacian is presented to evaluate the two-dimensional invariant and noise resistant properties of the proposed feature extraction. Experiments with still images and noisy images are provided to verify the effectiveness of the proposed approach in practice.

2D invariant object recognition using Log-Polar transform

Image registration is an essential step in many image processing applications that need visual information from multiple images for comparison, integration or analysis. Recently researchers have introduced image processing techniques using the log-polar transform (LPT) for its rotation and scale invariant properties. However, limitations still exist when LPT is applied to image registration applications. The major thesis of this dissertation is to provide in depth analysis of LPT, its advantages, and problems. We introduce new formulations that are derived to overcome the limitations of LPT and thus extend its horizon in practice. A novel techniques are proposed to address the limitations.
The first extension to be introduced is to extend the use of LPT to 2D object recognition application. Motivated by the observation that LPT is sensitive to translation, which leads to high computation in the search process, we integrate the combination of feature extraction and feature point screening method to the recognition system. With the scale and rotation invariant properties of LPT and the low computation feature extraction and screening approach that further reduces the number of feature point, a 2D object recognition is presented. 
The second limitations of LPT that is addressed in this dissertation is the nonuniform sampling and its effects. LPT suffers from nonuniform sampling which makes it not suitable for applications in which the registered images are altered or occluded. Inspired by this fact, we presents a new registration algorithm that addresses the problems of the conventional LPT while maintaining the robustness to scale and rotation. We introduce a novel Adaptive Polar Transform (APT) technique that evenly and effectively samples the image in the Cartesian coordinates. Combining APT with an innovative projection transform along with a matching mechanism, the proposed method yields less computational load and more accurate registration than that of the conventional LPT. Translation between the registered images is recovered with the new search scheme using Gabor feature extraction to accelerate the localization procedure. Moreover an image comparison scheme is proposed for locating the area where the image pairs differ. Experiments on real images demonstrate the effectiveness and robustness of the proposed approach for registering images that are subjected to occlusion and alteration in addition to scale, rotation and translation. 
Lastly, this dissertation observes the accuracy of the LPT approach that is limited by the number of samples used in the mapping process. Since obtaining scale and rotation parameters involves 2D correlation method either in the spatial domain or in the frequency domain, the computational complexity of the matching procedure grows exponentially as the number of samples increases. Motivated by this limitation, we propose a novel pre-shifted logarithmic spiral (PSLS) approach that is robust to translation, scale, and rotation and requires lower computational cost. By pre-shifting the sampling point in the angular direction by π/nt radian, the total number of samples in angular direction can be reduced by half. This yields great reduction in computational load in the matching process. Experimental results demonstrate the effectiveness and robustness of the proposed approach.

Studies on log-polar transform for image registration and improvements using adaptive sampling and logarithmic spiral

Image registration is an essential step in many image processing applications that need visual information from multiple images for comparison, integration or analysis. Recently researchers have introduced image registration techniques using the log-polar transform (LPT) for its rotation and scale invariant properties. However, the accuracy of the approach limits by the number of samples used in the mapping process, which affects directly the computational cost. Motivated by the success of LPT based approach and its limitation, we propose a novel Projective Polar Transform (PPT) based image registration method that is robust to translation, scale, and rotation and yields high accuracy while requires low computational cost. Unlike LPT that 2D interpolation is needed in the mapping process, our method uses one-to-one mapping mechanism that directly arranges image from Cartesian to Polar coordinate according to pre-computed PPT map. An innovative projection mechanism is proposed to reduce the image from two to one dimensional vectors. With the proposed approach, the mapping procedure is accelerated and the matching process can be performed in 1D. This results in great reduction of the computational cost.

R. Matungka

Papers

Image Registration Using Adaptive Polar Transform

Image registration using Adaptive Polar Transform

2D invariant object recognition using Log-Polar transform

Studies on log-polar transform for image registration and improvements using adaptive sampling and logarithmic spiral

Aerial image registration using Projective Polar Transform