Color Subspaces as Photometric Invariants

Complex reflectance phenomena such as specular reflections confound many vision problems since they produce image ‘features’ that do not correspond directly to intrinsic surface properties such as shape and spectral reflectance. A common approach to mitigate these effects is to explore functions of an image that are invariant to these photometric events. In this paper we describe a class of such invariants that result from exploiting color information in images of dichromatic surfaces. These invariants are derived from illuminant-dependent ‘subspaces’ of RGB color space, and they enable the application of Lambertian-based vision techniques to a broad class of specular, non-Lambertian scenes. Using implementations of recent algorithms taken from the literature, we demonstrate the practical utility of these invariants for a wide variety of applications, including stereo, shape from shading, photometric stereo, material-based segmentation, and motion estimation.     

Dominant-subspace invariants

Object recognition requires robust and stable features that are unique in feature space. Lie group analysis provides a constructive procedure to determine such features, called invariants, when they exist. Absolute invariants are rare in general, so quasi-invariants relax the restrictions required for absolute invariants and, potentially, can be just as useful in real-world applications. The paper develops the concept of a dominant-subspace invariant, a particular type of quasi-invariant, using the theory of Lie groups. A constructive algorithm is provided that fundamentally seeks to determine an integral submanifold which, in practice, is a good approximation to the orbit of the Lie group action. This idea is applied to the long-wave infrared problem and experimental results are obtained supporting the approach. Other application areas are cited     

Geometric and illumination invariants for object recognition

We propose invariant formulations that can potentially be combined into a single system. In particular, we describe a framework for computing invariant features which are insensitive to rigid motion, affine transform, changes of parameterization and scene illumination, perspective transform, and view point change. This is unlike most current research on image invariants which concentrates on either geometric or illumination invariants exclusively. The formulations are widely applicable to many popular basis representations, such as wavelets, short-time Fourier analysis, and splines. Exploiting formulations that examine information about shape and color at different resolution levels, the new approach is neither strictly global nor local. It enables a quasi-localized, hierarchical shape analysis which is rarely found in other known invariant techniques, such as global invariants. Furthermore, it does not require estimating high-order derivatives in computing invariants (unlike local invariants), whence is more robust. We provide results of numerous experiments on both synthetic and real data to demonstrate the validity and flexibility of the proposed framework     

Moment invariants for recognition under changing viewpoint and illumination

Generalised color moments combine shape and color information and put them on an equal footing. Rational expressions of such moments can be designed, that are invariant under both geometric deformations and photometric changes. These generalised color moment invariants are effective features for recognition under changing viewpoint and illumination. The paper gives a systematic overview of such moment invariants for several combinations of deformations and photometric changes. Their validity and potential is corroborated through a series of experiments. Both the cases of indoor and outdoor images are considered, as illumination changes tend to differ between these circumstances. Although the generalised color moment invariants are extracted from planar surface patches, it is argued that invariant neighbourhoods offer a concept through which they can also be used to deal with 3D objects and scenes.     

Moment forms invariant to rotation and blur in arbitrary number of dimensions

We present the construction of combined blur and rotation moment invariants in arbitrary number of dimensions. Moment invariants to convolution with an arbitrary centrosymmetric filter are derived first, and then their rotationally invariant forms are found by means of group representation theory to achieve the desired combined invariance. Several examples of the invariants are calculated explicitly to illustrate the proposed procedure. Their invariance, robustness, and capability of using in template matching and in image registration are demonstrated on 3D MRI data and 2D indoor images.     

Adaptive image segmentation by combining photometric invariantregion and edge information

An adaptive image segmentation scheme is proposed employing the Delaunay triangulation for image splitting. The tessellation grid of the Delaunay triangulation is adapted to the semantics of the image data by combining region and edge information. To achieve robustness against imaging conditions (e.g. shading, shadows, illumination and highlights), photometric invariant similarity measures and edge computation are proposed. Experimental results on synthetic and real images show that the segmentation method is robust to edge orientation, partially weak object boundaries and noisy-but-homogeneous regions. Furthermore, the method is robust, to a large degree, to varying imaging conditions     

一种基于投影不变量的目标跟踪方法

提出了一种基于平面投影不变量的目标跟踪算法．算法从图像中提取直线边缘计算投影不变量，用于对目标建模并跟踪．为提取直线边缘，使用改进的序列细化算法将边缘细化为单像素宽，而后用一种快速曲率估计方法估算边缘点的曲率，并保留估算值很小（约等于零）的点拟合直线．在所得直线族中按照邻近规则或者窗口规则挑选直线计算投影不变量．图像处理实验给出了用文中提出的图像预处理算法获得的直线边缘效果，并通过使用所得直线计算不变量的值衡量了所得不变量的稳定性和视角不变性．跟踪实验检验了跟踪算法的鲁棒性和实用性．     

基于步态能量图和不变矩的身份识别算法

分析步态能量图即具有作为静态的外观特征,又包含了识别的动力学有用信息,同时证明了步态能量图对噪声的不敏感性。文章提出了一种基于步态能量图和不变矩的身份识别算法,介绍了不变矩的基本理论以及Hu提出的七个不变矩,利用图像不变矩的平移、尺度和旋转不变特性,从原始的步态能量图中提取不变矩特征作为步态能量图的输入特征向量,运用不变矩的最小距离分类器的模式匹配进行步态特征分类。最后在CASIA步态数据库上对所提出的算法和其他新的步态识别方法相比较。实验结果表明,提出的算法是一种有效的步态识别方法。     

Model-based recognition of 3D objects from single images

In this work, we treat major problems of object recognition which have received relatively little attention lately. Among them are the loss of depth information in the projection from a 3D object to a single 2D image, and the complexity of finding feature correspondences between images. We use geometric invariants to reduce the complexity of these problems. There are no geometric invariants of a projection from 3D to 2D. However, given certain modeling assumptions about the 3D object, such invariants can be found. The modeling assumptions can be either a particular model or a generic assumption about a class of models. Here, we use such assumptions for single-view recognition. We find algebraic relations between the invariants of a 3D model and those of its 2D image under general projective projection. These relations can be described geometrically as invariant models in a 3D invariant space, illuminated by invariant “light rays,” and projected onto an invariant version of the given image. We apply the method to real images     

Invariants of six points and projective reconstruction from threeuncalibrated images

There are three projective invariants of a set of six points in general position in space. It is well known that these invariants cannot be recovered from one image, however an invariant relationship does exist between space invariants and image invariants. This invariant relationship is first derived for a single image. Then this invariant relationship is used to derive the space invariants, when multiple images are available. This paper establishes that the minimum number of images for computing these invariants is three, and the computation of invariants of six points from three images can have as many as three solutions. Algorithms are presented for computing these invariants in closed form. The accuracy and stability with respect to image noise, selection of the triplets of images and distance between viewing positions are studied both through real and simulated images. Applications of these invariants are also presented. Both the results of Faugeras (1992) and Hartley et al. (1992) for projective reconstruction and Sturm's method (1869) for epipolar geometry determination from two uncalibrated images with at least seven points are extended to the case of three uncalibrated images with only six points     

Colour invariants under a non-linear photometric camera model and their application to face recognition from video

Illumination invariance remains one of the most researched, yet the most challenging aspect of automatic face recognition. In this paper the discriminative power of colour-based invariants is investigated in the presence of large illumination changes between training and query data, when appearance changes due to cast shadows and non-Lambertian effects are significant. Specifically, there are three main contributions: (i) a general photometric model of the camera is described and it is shown how its parameters can be estimated from realistic video input of pseudo-random head motion, (ii) several novel colour-based face invariants are derived for different special instances of the camera model, and (iii) the performance of the largest number of colour-based representations in the literature is evaluated and analysed on a database of 700 video sequences. The reported results suggest that: (i) colour invariants do have a substantial discriminative power which may increase the robustness and accuracy of recognition from low resolution images in extreme illuminations, and (ii) that the non-linearities of the general photometric camera model have a significant effect on recognition performance. This highlights the limitations of previous work and emphasizes the need to assess face recognition performance using training and query data which had been captured by different acquisition equipment.     

图像不变矩的推广

该文提出了一种快速有效的推导不变矩的方法——三角函数生成法，建立了一种不变矩空间，总结出不变矩的一般构造规律，导出了5个新的不变矩表达式C8～C12其它高阶不变矩表达形式也可采用类似的构造方案．在此基础上还得出多种高阶不变矩的表达通式，讨论了不变矩的反射变换特性．并在实验中给出了离散情况下一些图像不变矩的稳定性比较．利用扩充后的不变矩特征集能更准确地对图像进行分类和识别．     

Degraded image analysis: an invariant approach

Analysis and interpretation of an image which was acquired by a nonideal imaging system is the key problem in many application areas. The observed image is usually corrupted by blurring, spatial degradations, and random noise. Classical methods like blind deconvolution try to estimate the blur parameters and to restore the image. We propose an alternative approach. We derive the features for image representation which are invariant with respect to blur regardless of the degradation PSF provided that it is centrally symmetric. As we prove in the paper, there exist two classes of such features: the first one in the spatial domain and the second one in the frequency domain. We also derive so-called combined invariants, which are invariant to composite geometric and blur degradations. Knowing these features, we can recognize objects in the degraded scene without any restoration     

Determination of blur and affine combined invariants by normalization

The determination of invariant characteristics is an important problem in pattern recognition. In many situations, images to be processed are usually subjected to geometric distortion and/or blur degradation. In this paper, we introduce an approach to derive blur and affine combined invariants (BAI). Firstly, we normalize the image to a standard form by using blur invariant moments as normalization constraints. Then, we construct the blur and affine combined invariants at the standard form. Using the method proposed in this paper, a set of blur and affine combined invariant features can be obtained easily and effectively. Several experimental results are presented to illustrate the performance of the invariants for simultaneously affine deformed and blur degraded images.