Explicit Separable two dimensional Moment Invariants for object recognition

Rotation and translation invariants of Gaussian–Hermite moments

Orthogonal invariant Lagrange-Fourier moments for image recognition

Design of orthogonal moment invariants for images with N-Fold rotation symmetry

Affine moment invariants are widely used in pattern recognition, most of the existing affine moment invariants are based on geometric central moments or continuous orthogonal moments. This paper proposes an approach to construct a set of discrete Tchebichef moment invariants which are simultaneously invariant to affine transformation and to convolution with circularly symmetric point spread function. Some important properties of proposed invariants are presented and proved. These invariants are used for image recognition. The experimental results show that the proposed method has better performance in pattern recognition compared to existing method.

The use of 3D discrete orthogonal invariant moments as descriptors of images constitutes one of the hot topics in the field of 3D image analysis, especially in the recognition and classification of deformed objects, due to their high numerical precision and low computing complexity. The TSR (translation, scale and rotation) invariant functions of discrete orthogonal moments can be obtained by expressing them as a linear combination of the corresponding invariant of geometric moments. This classical method is very expensive in time due to the long time allocated to compute the polynomial coefficients when complex or large 3D images are used. This main drawback eliminates the use of these moments in the recognition and classification fields of 3D objects. In this article, we propose a fast and efficient method for calculating 3D discrete orthogonal invariant moments of Hahn, Tchebichef, Krawtchouk, Meixner and Charlier of 3D image. This proposed method is based on the extraction of the 3D discrete orthogonal invariant moments from the 3D geometric invariant moments of the entire 3D image, using the 3D image cuboid representation (ICR) strategy, where each cuboid is treated independently. The proposed method has the advantage of accelerating the process of extracting the 3D discrete invariant moments compared with the classical method. The performance of the proposed method is evaluated in terms of the calculation time and classification accuracy using a set of 3D images. Instead of some examples of using the discrete orthogonal invariant moments of Hahn, Tchebichef, Krawtchouk, Meixner and Charlier as pattern features for pattern classification are also provided.

Functions of Moments that are invariant under geometric transformations are useful for image analysis and pattern recognition. The basic model of computer vision is projective transformation. Yet it is known that moment invariants for general projective transformations do not exist. This paper presents a novel method to derive moment invariants under restricted projective transformations. The form of the moment invariants is in a ratio of two determinants of moments. We first derive the relative moment invariants relating moments of the transformed image and moments of the original image. Then the absolute moment invariant is obtained by cancellation of the factors. The method is straightforward and extendible.

Geometric moment invariants to spatial transform and N-fold symmetric blur

It is known that the rotation, scaling and translation invariant property of image moments has a high significance in image recognition. For this reason, the seven invariant moments presented by Hu are widely used in the field of image analysis. These moments are of finite order; therefore, they do not comprise a complete set of image descriptors. For this reason, we introduce in this paper another series of invariant moments of infinite order, which are based on normalized central moments. The non-orthogonal property of these moments causes the redundancy of information. To overcome this problem, we propose a new construction technique of non-separable orthogonal polynomials in two variables based on a recurrence formula and we present a new set of orthogonal moments, which are invariant to translation, scaling and rotation. The presented approaches are tested in several well-known computer vision datasets including moment’s invariability, image retrieval and classification of objects, this latter based on fuzzy K-means clustering algorithm. The performance of these invariant moments for classification and image retrieval is compared with some recent invariant moments such as invariants of multi-channel orthogonal radial-substituted Chebyshev moments, invariants of quaternion radial-substituted Chebyshev moments, invariants of rotational moments in Radon space and Legendre–Fourier moments in Radon space. The experimental results made using four databases of images, namely Columbia Object Image Library (COIL-20) database, MPEG7-CE shape database, COIL-100 database and ORL database, show that our orthogonal invariant moments have done better than the other descriptors tested.

The orthogonal moments are giving relevant results of these last years within the framework of object detection, pattern recognition and image reconstruction. This article is based on orthogonal functions called "Orthogonal Mountain functions (OMFs)" and we introduce a new set of moments called the multichannel Mountain Fourier moments (MMFMs), their performance is in reconstruction, noise invariants, rotation, scale and translation for image color. To validate these proposed techniques, we made several experimental tests to analyse images. We compare the results obtained from invariant moments and other current orthogonal invariant moments; the experiments show the power of the proposed moments.

The extraction of feature vectors of the images is the most important step in image recognition, because it allows a good description of the forms to be recognized. This step is an operation that makes it possible to convert an image into a vector of real or complex values that can serve as a signature for this image. For an accurate recognition system, the used feature vector must be invariant to the three image transformations (translation, rotation and scale), which means that, the descriptor vectors of the image and the transformed image by translation, rotation or scale must be equal. Given the importance of moments and their invariants in pattern recognition and imaging, based on Newton’s binomial and trinomial formulas and the normalized central moments, we construct in this paper four new series of moments for 2D and 3D image recognition, which are invariant to translation, scaling and rotation (TSR): the first is a set of non-orthogonal moment invariants for 2D images (2dMIs), the second is a set of orthogonal moment invariants for 2D images (2dOMIs), the third is a set of non-orthogonal moment invariants for 3D images (3dMIs) and the fourth is a set of orthogonal moment invariants for 3D images (3dOMIs). Using the proposed invariant moments (2dMIs), (2dOMIs), (3dMIs) and (3dOMIs), we construct two types of image descriptor vectors for 2D images and two types for 3D images, which are invariant to translation, rotation and scale. A series of experiments is performed to validate this new set of invariant moments and compare its performance with the existing invariants moments. The obtained results ensure the superiority of the proposed moments over all existing moments in image recognition. Experiments on processing time show that the proposed method is faster than the existing orthogonal invariant moments.

The shape features of objects (connected components) in binary images are very important for image analysis, pattern (object) recognition, and computer vision. Conventional algorithms for calculating the shape features of objects in binary images can only calculate the shape features of objects without holes. This paper presents an algorithm or calculating the shape features of objects in binary images with holes. Based on a contour-tracing-based connected-component labeling algorithm, our proposed algorithm can calculate the number of objects, the number of holes, the Euler number in a binary image, extract the contours of objects, and calculate the area, perimeter, circularity, centroid of each object. Our proposed algorithm is able to make a contribution to image analysis, pattern recognition, and computer vision.

The aim of the following study was to examine the influence of image resolution in the pattern recognition in the grey scale images. In order to recognise the pattern, the authors used the method based on moment invariants which were the elements of feature vectors defining the features of the recognised object. The paper presents the influence of image resolution for exemplary images on both: the values of moment invariants and distances between feature vectors. The authors have paid a great attention to the fact that these distances are significant for distinguishing given object classes. One can conclude from the results that for a significant decrease in resolution there occur problems in pattern recognition. It results from the influence of image resolution on the value of moment invariants and at the same time on the value of the distance between the feature vectors defining the recognised objects. In this way, the paper shows that in order to recognise objects correctly, it is necessary to retain some necessary minimum resolution. It is indispensable despite the fact that we usually aim at decreasing the amount of processed data which is on the hand crucial because of short processing times in many practical applications. It is therefore essential because of the fact that we need to guarantee short times of image processing in many practical applications. Moreover, this study presents the examples of the algorithms in use.

Fast computation of accurate Gaussian–Hermite moments for image processing applications

Crowd counting is considered a challenging issue in computer vision. One of the most critical challenges in crowd counting is considering the impact of scale variations. Compared with other methods, better performance is achieved with CNN-based methods. However, given the limit of fixed geometric structures, the head-scale features are not completely obtained. Deformable convolution with additional offsets is widely used in the fields of image classification and pattern recognition, as it can successfully exploit the potential of spatial information. However, owing to the randomly generated parameters of offsets in network initialization, the sampling points of the deformable convolution are disorderly stacked, weakening the effectiveness of feature extraction. To handle the invalid learning of offsets and the inefficient utilization of deformable convolution, an offset-decoupled deformable convolution (ODConv) is proposed in this paper. It can completely obtain information within the effective region of sampling points, leading to better performance. In extensive experiments, average MAE of 62.3, 8.3, 91.9, and 159.3 are achieved using our method on the ShanghaiTech A, ShanghaiTech B, UCF-QNRF, and UCF_CC_50 datasets, respectively, outperforming the state-of-the-art methods and validating the effectiveness of the proposed ODConv.

Facial Expression (FE) detection is a popular research area, particularly in the field of Image Classification, Pattern Recognition and Computer Vision. Sparse Representation (SR) and Dictionary Learning (DL) have significantly enhanced the classification performance of image recognition and also resolved the problem of the nonlinear distribution of face images and its implementation with DL. However, the locality structure of face image data containing more discriminative information, which is very critical for classification has not been fully explored by state-of-the-art existing SR-based approaches. Furthermore, similar coding results between test samples and neighboring training data, contained in the feature space are not being fully realized from the image features with similar image categorizations, to effectively capture the embedded discriminative information. In an attempt to resolve the forgoing issues, we propose a novel DL method, Convolutional locality-sensitive Dictionary Learning (CLSDL) for Facial Expression detection.