Paraperspective ≡ affine

It is shown that the set of all paraperspective images with arbitrary reference point and the set of all affine images of a 3-D object are identical. Consequently, all uncalibrated paraperspective images of an object can be constructed from a 3-D model of the object by applying an affine transformation to the model, and every affine image of the object represents some uncalibrated paraperspective image of the object. It follows that the paraperspective images of an object can be expressed as linear combinations of any two non-degenerate images of the object. When the image position of the reference point is given the parameters of the affine transformation (and, likewise, the coefficients of the linear combinations) satisfy two quadratic constraints. Conversely, when the values of parameters are given the image position of the reference point is determined by solving a bi-quadratic equation.     

无标记印刷品质量在线检测方法研究

印刷品图像配准是实现印刷品自动检测的关键技术。以高分辨率印刷品图像为研究对象,将原始图像分割成多个兴趣区域,将兴趣区域的中心坐标与旋转角作为图像配准参数,通过变步长搜索算法获取被测图像与模板图像之间的最小旋转角;通过仿射变换将待检图像与模板图像进行配准并使用双向差影法计算两者的差影图像;通过二值化阈值与缺陷区域面积阈值进行缺陷识别。实验结果显示：该检测系统对合格品的检测准确率为96%,对不合格品的检测准确率为94%。     

Object recognition by combining paraperspective images

This paper provides a study on object recognition under paraperspective projection. Discussed is the problem of determining whether or not a given image was obtained from a 3-D object to be recognized. First it is clarified that paraperspective projection is the first-order approximation of perspective projection. Then it is shown that, if we represent an object as a set of its feature points and the object undergoes a rigid transformation or an affine transformation, any paraperspective image can be expressed as a linear combination of several appropriate paraperspective images: we need at least three images for rigid transformations; whereas we need at least two images for affine transformations. Particularly in the case of a rigid transformation, the coefficients of the combination have to satisfy two conditions: orthogonality and norm equality. A simple algorithm to solve the above problem based on these properties is presented: a linear, single-shot algorithm. Some experimental results with synthetic images and real images are also given.This work was done while the author was with ATR Auditory and Visual Perception Research Laboratories.Advanced Research Laboratory Hitachi, Ltd.     

一种基于正则化和Watson 视觉模型的图像指纹算法

大量多媒体应用的发展使得数字图像很容易地被非法操作和篡改,提出一种基于 图像正则化和视觉特性的图像指纹算法,可以有效地实现图像的认证和识别。首先对图像进行 正则化预处理,消除几何形变对图像的影响,然后对图像进行分块DCT 变换,利用Watson 视 觉模型对DCT 系数进行处理,增大人眼敏感的频域系数在计算图像特征时的权重,经过量化形 成最终的指纹序列。在图像指纹序列生成过程中,加入密钥控制,提高了指纹的安全性。实验 结果表明,该方法的冲突概率在10–7 数量级,对JPEG 压缩、旋转、缩放等操作具有较好的稳 健性。     

Continuous Time Matching Constraints for Image Streams

Corresponding image points of a rigid object in a discrete sequence of images fulfil the so-called multilinear constraint. In this paper the continuous time analogue of this constraint, for a continuous stream of images, is introduced and studied. The constraint links the Taylor series expansion of the motion of the image points with the Taylor series expansion of the relative motion and orientation between the object and the camera. The analysis is done both for calibrated and uncalibrated cameras. Two simplifications are also presented for the uncalibrated camera case. One simplification is made using an affine reduction and the so-called kinetic depths. The second simplification is based upon a projective reduction with respect to the image of a planar configuration. The analysis shows that the constraint involving second-order derivatives are needed to determine camera motion. Experiments with real and simulated data are also presented.     

A Linear Algorithm for Computing the Homography from Conics in Correspondence

This paper presents a study, based on conic correspondences, on the relationship between two perspective images acquired by an uncalibrated camera. We show that for a pair of corresponding conics, the parameters representing the conics satisfy a linear constraint. To be more specific, the parameters that represent a conic in one image are transformed by a five-dimensional projective transformation to the parameters that represent the corresponding conic in another image. We also show that this transformation is expressed as the symmetric component of the tensor product of the transformation based on point/line correspondences and itself. In addition, we present a linear algorithm for uniquely determining the corresponding point-based transformation from a given conic-based transformation up to a scale factor. Accordingly, conic correspondences enable us to easily handle both points and lines in uncalibrated images of a planar object.     

A Unified Theory of Uncalibrated Stereo for Both Perspective and Affine Cameras

This paper addresses the recovery of structure and motion from uncalibrated images of a scene under full perspective or under affine projection. Particular emphasis is placed on the configuration of two views, while the extension to $N$ views is given in Appendix. A unified expression of the fundamental matrix is derived which is valid for any projection model without lens distortion (including full perspective and affine camera). Affine reconstruction is considered as a special projective reconstruction. The theory is elaborated in a way such that everyone having knowledge of linear algebra can understand the discussion without difficulty. A new technique for affine reconstruction is developed, which consists in first estimating the affine epipolar geometry and then performing a triangulation for each point match with respect to an implicit common affine basis.     

基于深度信息与尺度空间的仿射不变特征检测*

介绍了一种利用深度信息的仿射区域检测器。这种方法在视角变换的情况下能自动检测出图景中同一物理区域,为后续的识别算法提供了坚实的特征检测基础,在计算机视觉领域有广阔的应用前景。该方法是基于尺度空间理论,这个理论已经在自动尺度选择中有较成熟的应用。提出了利用深度信息估计出3D物体模型的算法,并生成相应的仿射不变的高斯尺度空间,并给出从3D到2D的投射变换的高精度估计方法,以补偿投射变换造成的扭曲形变。因此对特征检测的可靠性将有明显的提高。为了评估本算法的鲁棒性,进行了不同视角的真实图片与合成图片的实验,并与其     

Shape matching using LAT and its application to handwritten numeralrecognition

This paper describes an iterative technique for gradually deforming a mask binary image with successive local affine transformation (LAT) operations so as to yield the best match to an input binary image as one new and promising approach toward robust handwritten character recognition. The method uses local shapes in the sense that the LAT of each point at one location is optimized using locations of other points by means of least-squares data fitting using Gaussian window functions. It also uses a multiscale refinement technique that decreases the spread of window functions with each iteration. Especially in handwritten character recognition, structural information is indispensable for robust shape matching or discrimination. The method is enhanced to explicitly incorporate structures by weighting the above least-squares criterion with similarity measures of both topological and geometric features of the mask and input images. Moreover, deformation constraints are imposed on each iteration, not only to promote and stabilize matching convergence but also to suppress an excessive matching process. Shape matching experiments have been successfully carried out using skeletons of totally unconstrained handwritten numerals     

A Frequency Domain Technique Based on Energy Radial Projections for Robust Estimation of Global 2D Affine Transformations

The contribution of this paper is twofold: (1) it provides a thorough analysis of the frequency domain relationships relating two affine-warped images and (2) based on a fundamental equation between energy radial projections, it presents an original algorithm for estimating the global 2D affine transformation between the two images. It is well known that operating in the frequency domain allows one to separate the estimate of the affine matrix, related to the magnitudes of the Fourier transforms of the two images, from the estimate of the translation vector, related to their phases. Exploiting this property, our algorithm consists of two main steps: (1) the affine matrix is first estimated by solving, with a coarse-to-fine strategy, a suitable minimization problem formulated upon the radial projections of the image energies, and (2) after compensation for the contribution of the affine matrix, the translation vector is then recovered by means of phase correlation. The proposed method is very robust against perspective distortion and, with moderate translational displacements, it may also work when the two images differ along their peripheral areas. Experimental evidence of these characteristics is reported and discussed. The algorithm can be efficiently implemented via FFT and well suits applications requiring unsupervised and/or quasi-real-time estimation of global motion that can be described with 2D affine transformations.     

基于低秩矩阵分解的批量扫描文档图像纠偏

扫描文档图像纠偏的关键是对图像偏转角度进行快速准确的估计。传统的基于图片自身纹理结构的算法,如Hough变换、Radon变换,不仅易受文档自身特殊结构或噪声影响,而且单幅图像纠偏的平均耗时较长。提出了一种基于低秩矩阵分解理论扫描文档图像的批量纠偏方法,该方法将批量图像构造成一个较大的矩阵,通过迭代对每一列进行适当地旋转,达到矩阵具有较低秩的目的,进而实现对每副图像偏转角度的恰当估计及纠偏。实验结果表明,该方法不仅具有较高纠偏的精度,而且单幅图片的平均耗时也小于现有的图片纠偏算法。     

A feature-based technique for joint, linear estimation ofhigh-order image-to-mosaic transformations: mosaicing the curved humanretina

An algorithm for constructing image mosaics from multiple, uncalibrated, weak-perspective views of the human retina is presented and analyzed. It builds on an algorithm for registering pairs of retinal images using a noninvertible, 12-parameter, quadratic image transformation model and hierarchical, robust estimation. The major innovation presented is a linear, feature-based, noniterative method for jointly estimating consistent transformations of all images onto the mosaic "anchor image." Constraints for this estimation are derived from pairwise registration both directly with the anchor image and indirectly between pairs of nonanchor images. An incremental, graph-based technique constructs the set of registered image pairs used in the solution. The estimation technique allows images that do not overlap the anchor frame to be successfully mosaiced, a valuable capability for mosaicing images of the retinal periphery. Experimental analysis on data sets from 16 eyes shows the average overall median transformation error in final mosaic to be 0.76 pixels. The technique is simpler, more accurate, and offers broader coverage than previously published methods     

Depth recovery and affine reconstruction under camera pure translation

This paper addresses the problems of depth recovery and affine reconstruction from two perspective images, which are generated by an uncalibrated translating camera. Firstly, we develop a new constraint that the homography for the plane, which is orthogonal to the optical axis, is determined only by the epipole and the plane's relative distance to the origin under camera pure translation. The algorithm of depth recovery is based on this new constraint, and it can successfully avoid the step of camera calibration. With the recovered depth, we show that affine reconstruction can be obtained readily. The proposed affine reconstruction does not need any control points, which were used to expand the affine coordinate system in existing method. Therefore, it could avoid the step of non-planarity verification as well as the errors from the control points. Error analysis is also presented to evaluate the uncertainty for the recovered depth value. Finally, we have tested the proposed algorithm with both simulated data and real image data. And the results show that the proposed algorithm is accurate and practical.     

Accurate and robust localization of duplicated region in copy–move image forgery

Copy–move image forgery detection has recently become a very active research topic in blind image forensics. In copy–move image forgery, a region from some image location is copied and pasted to a different location of the same image. Typically, post-processing is applied to better hide the forgery. Using keypoint-based features, such as SIFT features, for detecting copy–move image forgeries has produced promising results. The main idea is detecting duplicated regions in an image by exploiting the similarity between keypoint-based features in these regions. In this paper, we have adopted keypoint-based features for copy–move image forgery detection; however, our emphasis is on accurate and robust localization of duplicated regions. In this context, we are interested in estimating the transformation (e.g., affine) between the copied and pasted regions more accurately as well as extracting these regions as robustly by reducing the number of false positives and negatives. To address these issues, we propose using a more powerful set of keypoint-based features, called MIFT, which shares the properties of SIFT features but also are invariant to mirror reflection transformations. Moreover, we propose refining the affine transformation using an iterative scheme which improves the estimation of the affine transformation parameters by incrementally finding additional keypoint matches. To reduce false positives and negatives when extracting the copied and pasted regions, we propose using “dense” MIFT features, instead of standard pixel correlation, along with hysteresis thresholding and morphological operations. The proposed approach has been evaluated and compared with competitive approaches through a comprehensive set of experiments using a large dataset of real images (i.e., CASIA v2.0). Our results indicate that our method can detect duplicated regions in copy–move image forgery with higher accuracy, especially when the size of the duplicated region is small.     

Homography and Fundamental Matrix Estimation from Region Matches Using an Affine Error Metric

Matching a pair of affine invariant regions between images results in estimation of the affine transformation between the regions. However, the parameters of the affine transformations are rarely used directly for matching images, mainly due to the lack of an appropriate error metric of the distance between them. In this paper we derive a novel metric for measuring the distance between affine transformations: Given an image region, we show that minimization of this metric is equivalent to the minimization of the mean squared distance between affine transformations of a point, sampled uniformly on the image region. Moreover, the metric of the distance between affine transformations is equivalent to the l ₂ norm of a linear transformation of the difference between the six parameters of the affine transformations. We employ the metric for estimating homographies and for estimating the fundamental matrix between images. We show that both homography estimation and fundamental matrix estimation methods, based on the proposed metric, are superior to current linear estimation methods as they provide better accuracy without increasing the computational complexity.     

Quasi-perspective Projection Model: Theory and Application to Structure and Motion Factorization from Uncalibrated Image Sequences

This paper addresses the problem of factorization-based 3D reconstruction from uncalibrated image sequences. Previous studies on structure and motion factorization are either based on simplified affine assumption or general perspective projection. The affine approximation is widely adopted due to its simplicity, whereas the extension to perspective model suffers from recovering projective depths. To fill the gap between simplicity of affine and accuracy of perspective model, we propose a quasi-perspective projection model for structure and motion recovery of rigid and nonrigid objects based on factorization framework. The novelty and contribution of this paper are as follows. Firstly, under the assumption that the camera is far away from the object with small lateral rotations, we prove that the imaging process can be modeled by quasi-perspective projection, which is more accurate than affine model from both geometrical error analysis and experimental studies. Secondly, we apply the model to establish a framework of rigid and nonrigid factorization under quasi-perspective assumption. Finally, we propose an Extended Cholesky Decomposition to recover the rotation part of the Euclidean upgrading matrix. We also prove that the last column of the upgrading matrix corresponds to a global scale and translation of the camera thus may be set freely. The proposed method is validated and evaluated extensively on synthetic and real image sequences and improved results over existing schemes are observed.     

基于图分割与Hausdorff距离的多分辨率影像匹配

针对具有复杂场景的航拍图像提出了一种基于图分割理论与Hausdorff距离的多分辨率影像匹配方法。在高斯金字塔图像模型中,低分辨率的图像通过图分割方法,充分考虑图像中的局部和全局的信息,提取到稳定和完整的图像区域边界,并以区域边界作为待匹配的曲线。再通过计算曲线的统计特性作为图像间待匹配特征,并由信号相关的度量方法粗估计出图像间全局仿射变换参数。利用粗估计的参数在高分辨率层次上进一步通过基于Hausdorff距离的匹配方法搜索到精确的变换参数。实验结果表明,该方法在较大变形和强噪音干扰的情况下对复杂场景的图像也能有效地完成匹配。     

亚仿射变换的性质及其应用

数字图像的置乱技术是图像信息安全与隐藏的基础性工作，基于几何中仿射变换的思想，提出了一类可用于图像置乱技术的亚仿射交换，重点研究了亚仿射变换的性质，给出仿射变换是亚仿射变换的必要条件，讨论了亚仿射变换的周期性。实验结果表明：亚仿射变换有较好的置乱效果，从图像信息加密的安全性角度看，它优于Arnold,Fibonacci等几何置乱变换。     

An efficient contrast-enhancement method using the analog to digital converter

The study presents a hybrid method of contrast enhancement using the analog to digital converter (ADC) for use in high-speed industrial applications. The proposed framework processes the digitized image in efficient steps to generate the low and high offsets of the ADC. These offsets are used to modify the analog image signal by an affine transform, such that the digitization of the transformed signalis the enhanced image. Since the signal transformation is mostly done in the analog domain, the method is efficient, and its implementation is inexpensive. As an example, the enhancement method is used in applications where, given images of varying initial contrast, we can obtain an user-specified contrast for all images. These images are then segmented by a simpler image-processing algorithm. The method is a generalization of existing ADC-based enhancement methods and is compared experimentally to the digital domain techniques. An application of the method is given for the enhancement of laser-etched characters on industrial parts.