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Methods based on Convolutional neural network (CNN) have been effectively applied to object detection. However, the Traditional object detection models face huge obstacles in the field of the aerial scene due to the complexity of the aerial image and the wide degree of freedom of the remote sensing object in density, scale, and orientation. In this article, we applied rotatable bounding boxes (RBox) instead of the traditional bounding box (BBox) and improved the CNN-based network to effectively handle the oriented angle of the detected object so that the rotation invariant property can be achieved. Our model is trained and tested on 3 classes of remote sensing category Airplanes, ships, and Cars. Compared with two of the common benchmarks of the BBox methods Faster R-CNN and SDD, our model outperforms both of them. Where our model efficiently output the orientation angles of the detected objects.

Accurate built-up area (BA) information plays crucial role for many applications. PolSAR imagery can provide important source for BAs information analysis. However, the BAs with large orientation angles are usually misdetected as vegetation, and labeled BA samples with special orientations are diffi-cult to obtain. In this paper, a PolSAR BA extraction method based on eigenvalue statistical information and PU-Learning is proposed to overcome abovementioned problems. Firstly, the roll invariance of coherency-matrix eigenvalues and the building orientations have been analyzed. Then, by adopting eigenvalue-Wishart unsupervised classification, regional statistical information and rotation invariant property are comprehensively utilized. Finally, the BAs are extracted by combining PU-Learning classifier with only positive samples at same distinguishable orientation. Six experiments on PolSAR imageries show the accuracy of proposed method can reach 92-99% with only a few positive samples, 8-20% higher than classical model decomposition-based PU-Learning method, and the requirement for labeled samples is less than 0.65%.

Broad learning system (BLS) has been proposed as an alternative method of deep learning. The architecture of BLS is that the input is randomly mapped into series of feature spaces which form the feature nodes, and the output of the feature nodes are expanded broadly to form the enhancement nodes, and then the output weights of the network can be determined analytically. The most advantage of BLS is that it can be learned incrementally without a retraining process when there comes new input data or neural nodes. It has been proven that BLS can overcome the inadequacies caused by training a large number of parameters in gradient-based deep learning algorithms. In this paper, a novel variant graph regularized broad learning system (GBLS) is proposed. Taking account of the locally invariant property of data, which means the similar images may share similar properties, the manifold learning is incorporated into the objective function of the standard BLS. In GBLS, the output weights are constrained to learn more discriminative information, and the classification ability can be further enhanced. Several experiments are carried out to verify that our proposed GBLS model can outperform the standard BLS. What is more, the GBLS also performs better compared with other state-of-the-art image recognition methods in several image databases.

In this article, a robust attitude control scheme, which is called sliding mode control with unidirectional auxiliary surfaces (UAS-SMC), is proposed for the near-space vehicle with attitude constraints and time-varying unknown disturbance. Firstly, the positively invariant sets are designed with the UAS-SMC method. The invariant property of these sets can be utilized to guarantee the attitude constraints. Secondly, a UAS nonlinear disturbance observer is firstly developed for the NSV with time-varying unknown disturbance. By introducing the information of UAS surfaces, the performance of this observer is enhanced. The convergence of all closed-loop signals is rigorously proved via Lyapunov analysis method under the developed robust UAS-SMC scheme. Finally, simulation results are given to illustrate the effectiveness of the proposed attitude control scheme.

Safety is a fundamental issue in robotics, especially in the growing application of human-robot interaction (HRI), where collision avoidance is an important consideration. In this paper, a novel real-time velocity based collision avoidance planner is presented to address this problem. The proposed algorithm provides a solution to deal with both collision avoidance and reference tracking simultaneously. An invariant safe set is introduced to exclude the dangerous states that may lead to collision, and a smoothing function is introduced to adapt different reference commands and to preserve the invariant property of the safe set. A real-time experiment with a moving obstacle is conducted on FANUC LR Mate 200iD/7L.

In order to improve the rotation invariant property of the conventional template matching method, a novel template matching based on the polar coordinate was proposed. The origin of the polar coordinate was at the center of the template. And the matching result was central symmetry, which made the method have the translation and rotation invariant properties simultaneously. The recognition process was divided into two phased. In the first phase, gray information was used to complete matching calculation, and some candidate points were selected according to the matching result. In the second phase, edge strong matching of candidate points was completed. The candidate point, where the sum of gray matching value and edge strong matching value was minimal, was determined as the best matching point. Experiments results show that this method can meet the real-time requirement of the TV tracking system.

The wavelet moments are very useful image descriptors which contain both global and local characteristics of an image. Its usefulness is further characterized by rotation invariant property of its magnitude. The phase information is, however, left out because it changes with image rotation. In this paper, we incorporate phase information and use both the real and imaginary components of wavelet moments to describe an image and develop a similarity measure which is invariant under image rotation. The proposed framework is applied to face recognition. Extensive experimental results are provided to demonstrate the enhanced performance of the proposed framework as compared to the magnitude only framework. The results are also compared with many other state-of-the-art techniques used for face recognition.

We propose a polarization division multiplexed optical eigenvalue modulation scheme based on the invariant property of eigenvalue associated to Manakov equation. We numerically demonstrate the feasibility of the proposed scheme.

This paper contains a simplified framework for the analysis of sequences of images taken by uncalibrated cameras. It is assumed that the correspondences between the points in the different images are known. Corresponding points in a sequence of n images are related to each other by a fixed n-linear form. This form is an object invariant property, closely linked to the motion of the camera relative to the fixed world. We first describe a reduced setting in which these multilinear forms are easier to understand and analyse. This new formulation of the multilinear forms is then extended to the calibrated case and the traditional uncalibrated case, thus highlighting the similarities between the different settings. The framework is of importance as a theoretical tool for understanding the algebra of multiple view geometry, but it is also a basis for constructing linear algorithms for the recovery of structure and motion from image sequences. This is illustrated in experiments.

In this paper, we propose a framework that estimates the discrete intensity rank of a facial expression based on a single image. For most people, judging whether an expression is more intense than others is easier than determining its real-valued intensity degree, and hence the relative order of two expressions is more distinguishable than the exact difference between them. We utilize the relative order to construct an image-based ranking approach for inferring the discrete ranks. The challenge of image-based approaches is to conduct a representation for subtle expression changes. We employ an efficient descriptor, scattering transform, which is translation invariant and can linearize deformations. This scattering representation recovers the lost high frequencies and retains discrimination under invariant property. Our experimental results demonstrate that the proposed framework with scattering transform outperforms other compared feature descriptors and algorithms.

In this paper, we use a new method, which based on the spherical harmonics transform, to extract 3D ear rotation invariant feature from 3D ear data. And a 3D ear recognition system was built through matching ear spherical harmonics feature, which is rotation invariant in mathematical theory. Utilizing its rotation invariant property, the 3D ear recognition method could be strongly robust in pose variation. A Rank-1 recognition rate, achieved in experiment, is 96.4% on a data set of 415 subjects, and processing time also has been reduced, comparing to the well-known ICP algorithm.

In this work we assess the recently introduced Local Phase Quantization (LPQ) as textural descriptor for the problem of forest species recognition. LPQ is based on quantizing the Fourier transform phase in local neighborhoods and the phase can be shown to be a blur invariant property under certain commonly fulfilled conditions. We show through a series of comprehensive experiments that LPQ surpasses the results achieved by the widely used Local Binary Patterns (LPB) and its variants. Our experiments also show, though, that the results can be further improved by combining both LPB and LPQ. In this sense, several different combination strategies were tried out. Using a SVM classifiers, the combination of LPB and LPQ brought an improvement of about 7 percentage points on a database composed by 2,240 microscopic images extracted from 112 different forest species.

The use of autoregressive models in textual analysis holds great potential. Coupling the technique to a circular neighbourhood set imparts a rotational invariant property to it. This was demonstrated by Kashyap and Khotanzad in their model called the Circular Symmetric Autogressive (CSAR) Random Field model. The short-coming in this very ingenious proposal is that it is set in a background of square pixels and the rotational invariant property of the model fails in cases when the aspect ratio of the pixels are not at unity. This paper proposes a major modification to the CSAR to render the model rotational invariant under all configurations of pixel implementation. It is based on the area segments covered by a circle set in a 3×3 neighbourhood. We call it the Circular Area Autoregressive (CAAR) model. The results obtained from the CAAR showed much better consistency over that of the CSAR when a non-square pixel image was used.

In this paper, we propose a hybrid approach for addressing feature-based matching problem. We aim to obtain robust and accurate correspondence between features from image frames under unknown and unstructured environments. The approach incorporates image texture analysis, 2-D analytic signal theory and color modeling. It takes advantage of geometric invariant property in texture and monogenic signal information as well as photometric invariant property in HSV color information. The detected features are well localized with high accuracy and the selected matches are robust to changes in scale, blur, viewpoint, and illumination. Experiments conducted on a standard benchmark dataset demonstrate the effectiveness and reliability of our approach.

The idea of a phase-only matched filter [J. L. Horner and P. D. Gianino, Appl. Opt. 23, 812-816 (1984)] is incorporated in the scheme of circular harmonic component matched filtering [Y. N. Hsu and H. H. Arsenault, Appl. Opt. 21, 4016-4019 (1982)]. Computer simulation showed that the phase-only circular harmonic matched filter possesses the rotational invariant property for 2-D recognition. Furthermore, it does a better job in recognizing closely placed targets compared with traditional circular harmonic filters. The simulation also demonstrated that a pure phase circular harmonic filter is less liable to give rise to false alarms in recognition because the sidelobe produced by it is much less pronounced and much less extensive than that produced by a traditional circular harmonic filter.

In this article the status of colour as an invariant property of objects is addressed. It is explained that if the underlying physical determinants of colour are studied, it will be difficult to consider colour as an internal property of objects. The colour of objects is dependent on both the surface reflectance of incident light and the illumination. Whereas reflectance is a constant factor, the characteristics of the illumination are continuously changing. Therefore, it is surprising that the human perceiver succeeds in assigning colour to objects independent of the illumination. Theoretical developments as well as empirical findings concerning the colour constancy issue are discussed.

In this paper, we propose a new image demising method based on complex contourlet transform. The complex contourlet effectively incorporate the approximate shift invariant property of dual-tree complex transform and directionality and anisotropy of contourlet transform. We apply our methods to image denoising experiments on gray and color images, and compare it with other popular denoising schemes. Our experiments show that the proposed method outperforms the adaptive Wiener filter, the wavelet shrinkage denoising and the contourlet denoising both visually and in terms of the PSNR values, especially for images with high texture information.

In this paper, we introduce the concept of self-quotient image (SQI) for robust face recognition under varying lighting conditions. It is based on the quotient image method (Amnon Shashua et al., 2001) (T. Riklin-Raviv et al., 1999) to achieve lighting invariance. However, the SQI has three advantages: (1) it needs only one face image for extraction of intrinsic lighting invariant property of a face while removing extrinsic factor corresponding to the lighting; (2) no alignment is needed; (3) it works in shadow regions. The theoretical analysis on conditions where the algorithm is applicable and a non-iterative filtering algorithm for computing SQI are presented. Experiment results demonstrate the effectiveness of our method for robust face recognition under varying lighting conditions.

We examine the problem of computing shape descriptions from stereo, where by shape descriptions we mean 3-D volumetric descriptions of objects rather than a 2 /12-D depth map of the scene. We argue that intermediate 2 /12-D depth measurements may not be always directly available from stereo, especially when there are curved surfaces in the scene, and that 3-D volumetric descriptions of objects may have to be derived directly from stereo correspondences. We then present methods to recover volumetric shape from stereo using LSHGCs and SHGCs as the shape models. Our methods are based on some invariant properties of LSHGCs and SHGCs in their monocular and stereo projections. Experimental results on both synthetic and real images of objects with curved surfaces are given. Our technique allows dense surface descriptions to be recovered even for objects without much texture, and it is not restricted to narrow stereo angles or low resolution images. Our technique can also handle objects in close range where perspective distortion in the images can be significant.

A way to write proof scores showing that distributed systems have invariant properties in algebraic specification languages is described, which has been devised through several case studies. The way makes it possible to divide a formula stating an invariant property under discussion into reasonably small ones, each of which is proved by writing proof scores individually. This relieves the load to reduce logical formulas and can decrease the number of subcases into which the case is split in case analysis.

Recently, a time‐reversal mirror (or phase conjugate array) was demonstrated experimentally in the ocean, which spatially and temporally re‐focused an incident acoustic field back to the original position of the probe source. [Kuperman et al., accepted for publication in J. Acoust. Soc. Am.]. Here, this waveguide time‐reversal mirror technique is extended to refocus at ranges other than that of the probe source. This procedure is based on the acoustic‐field invariant property in the coordinates of frequency and range in an oceanic waveguide [G. A. Grachev, Acoust. Phys. 39(1), 33–35 (1993)]. This technique has been verified in a second phase conjugate experiment conducted in the Mediterranean Sea in May 1997. The theory behind variable range focusing will be presented along with experimental results demonstrating the ability to shift the focal range ±1 km for a probe source in the vicinity of 15 km from the source–receive array.

Recent time‐reversal mirror (TRM) experiments conducted in the Mediterranean Sea demonstrated variable range focusing using the frequency‐range invariant property in a shallow‐water waveguide [Song et al., J. Acoust. Soc. Am. 102, 3171(A) (1997)]. The technique involves retransmitting the data at a shifted frequency according to the desired change in focal range in almost real‐time fashion. As opposed to the variable range focusing, there does not appear to be an environmentally independent elegant solution for variable depth focusing. However, a method based on knowledge of the environment, which translates to being able to compute the acoustic modal structure, permits a focal depth shift. The method involves projecting out the important modes received at the vertical source–receive array (SRA) and appropriately altering their excitation to focus at another depth. In the May 1997 experiment, some limited results demonstrated that this method is feasible. Comparison of data with simulations and theoretical analysis will be presented and discussed. [Work supported by ONR.]

Three-month-old infants were habituated to two different motions of deformation, presented ‘live’ with an object of sponge rubber. After habituation, one-third of the subjects was presented with a third deforming motion; one-third was presented with a rigid motion of the same object; and the other third was presented with a continuation of the habituation sequence. The group presented with a rigid motion dishabituated, exhibiting a sharp increase in looking time. The other two groups showed little or no increase. These results suggest that infants perceive elasticity of substance, in contrast to rigidity, as an invariant property of an object over different deforming motions.

In a pure functional language a series of values computed from one another can be considered as different states of the same “abstract object”. For this abstract object temporal properties (e.g. invariants) can be formulated and proved. This paper explains how to define and prove certain kinds of temporal properties of programs written in the pure functional language Clean. Sparkle, a theorem prover designed for Clean, is applied as a tool. Since Sparkle is not capable of handling temporal logical properties, its original version has been extended to support object abstraction, certain temporal properties and a new form of theorems which includes hypotheses. The resulting system is called Sparkle-T. The examples presented in this paper illustrate how object abstraction and the definition and proof of temporal properties can be carried out in Sparkle-T. Furthermore, some novel features of the Sparkle-T system are demonstrated as well.

More and more attention has been paid to the invariant texture analysis, because the training and testing samples generally have not identical or similar orientations, or are not acquired from the same viewpoint in many practical applications, which often has negative influences on texture analysis. Local binary pattern (LBP) has been widely applied to texture classification due to its simplicity, efficiency, and rotation invariant property. In this paper, an integrated local binary pattern (ILBP) scheme including original rotation invariant LBP, improved contrast rotation invariant LBP, and direction rotation invariant LBP is proposed which can effectively overcome the deficiency of original LBP that is ignoring contrast and direction information. In addition, for surmounting another major drawback of LBP such as locality which can result in the lack of shape and space expression of the holistic texture image, Zernike moment features are fused into the improved LBP texture features in the proposed method because they comprise orthogonal and rotation invariant property and can be easily and rapidly calculated to an arbitrary high order. Experimental results show that the proposed method can be remarkably superior to the other state-of-the-art methods when rotation invariant texture features are extracted and classified.

An analysis of the broadband beamspace adaptive array is provided. There are two conditions imposed on the array. First, the individual beams should have a good frequency invariant property. Second, they should be linearly independent. However, these two conditions are not independent and it is shown that there is a trade-off between them. To improve the interference cancellation capability of the array, we may need to sacrifice the frequency invariant property of the beams to some degree for more linearly independent beams. A DFT-modulated design method is also proposed, where the beam directions are uniformly distributed over the spatial domain and the linear independence of the beams is guaranteed inherently. Simulation results verified our analysis and the proposed method.