Numerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term

In this paper, we consider the variable-order Galilei advection diffusion equation with a nonlinear source term. A numerical scheme with first order temporal accuracy and second order spatial accuracy is developed to simulate the equation. The stability and convergence of the numerical scheme are analyzed. Besides, another numerical scheme for improving temporal accuracy is also developed. Finally, some numerical examples are given and the results demonstrate the effectiveness of theoretical analysis. Keywords: The variable-order Galilei invariant advection diffusion equation with a nonlinear source term; The variable-order Riemann–Liouville fractional partial derivative; Stability; Convergence; Numerical scheme improving temporal accuracy

Position, rotation, and scale invariant recognition of images using higher-order spectra

A new approach to recognition of images using invariant features based on higher-order spectra is presented. Higher-order spectra are translation invariant because translation produces linear phase shifts which cancel. Scale and amplification invariance are satisfied by the phase of the integral of a higher-order spectrum along a radial line in higher-order frequency space because the contour of integration maps onto itself and both the real and imaginary parts are affected equally by the transformation. Rotation invariance is introduced by deriving invariants from the Radon transform of the image and using the cyclic-shift invariance property of the discrete Fourier transform magnitude. Results on synthetic and actual images show isolated, compact clusters in feature space and high classification accuracies

Scene invariant crowd counting

This paper describes a scene invariant crowd counting algorithm that uses local features to monitor crowd size. Unlike previous algorithms that require each camera to be trained separately, the proposed method uses camera calibration to scale between viewpoints, allowing a system to be trained and tested on different scenes. A pre-trained system could therefore be used as a turn-key solution for crowd counting across a wide range of environments. The use of local features allows the proposed algorithm to calculate local occupancy statistics, and Gaussian process regression is used to scale to conditions which are unseen in the training data, also providing confidence intervals for the crowd size estimate. A new crowd counting database is introduced to the computer vision community to enable a wider evaluation over multiple scenes, and the proposed algorithm is tested on seven datasets to demonstrate scene invariance and high accuracy. To the authors' knowledge this is the first system of its kind due to its ability to scale between different scenes and viewpoints.

Scene invariant crowd counting and crowd occupancy analysis

In public places, crowd size may be an indicator of congestion, delay, instability, or of abnormal events, such as a fight, riot or emergency. Crowd related information can also provide important business intelligence such as the distribution of people throughout spaces, throughput rates, and local densities. A major drawback of many crowd counting approaches is their reliance on large numbers of holistic features, training data requirements of hundreds or thousands of frames per camera, and that each camera must be trained separately. This makes deployment in large multi-camera environments such as shopping centres very costly and difficult. In this chapter, we present a novel scene-invariant crowd counting algorithm that uses local features to monitor crowd size. The use of local features allows the proposed algorithm to calculate local occupancy statistics, scale to conditions which are unseen in the training data, and be trained on significantly less data. Scene invariance is achieved through the use of camera calibration, allowing the system to be trained on one or more viewpoints and then deployed on any number of new cameras for testing without further training. A pre-trained system could then be used as a ‘turn-key’ solution for crowd counting across a wide range of environments, eliminating many of the costly barriers to deployment which currently exist.

Towards condition-invariant sequence-based route recognition

In this paper we present a novel algorithm for localization during navigation that performs matching over local image sequences. Instead of calculating the single location most likely to correspond to a current visual scene, the approach finds candidate matching locations within every section (subroute) of all learned routes. Through this approach, we reduce the demands upon the image processing front-end, requiring it to only be able to correctly pick the best matching image from within a short local image sequence, rather than globally. We applied this algorithm to a challenging downhill mountainbiking visual dataset where there was significant perceptual or environment change between repeated traverses of the environment, and compared performance to applying the feature-based algorithm FAB-MAP. The results demonstrate the potential for localization using visual sequences, even when there are no visual features that can be reliably detected.

Breast cancer detection from thermal images using bispectral invariant features

Highly sensitive infrared (IR) cameras provide high-resolution diagnostic images of the temperature and vascular changes of breasts. These images can be processed to emphasize hot spots that exhibit early and subtle changes owing to pathology. The resulting images show clusters that appear random in shape and spatial distribution but carry class dependent information in shape and texture. Automated pattern recognition techniques are challenged because of changes in location, size and orientation of these clusters. Higher order spectral invariant features provide robustness to such transformations and are suited for texture and shape dependent information extraction from noisy images. In this work, the effectiveness of bispectral invariant features in diagnostic classification of breast thermal images into malignant, benign and normal classes is evaluated and a phase-only variant of these features is proposed. High resolution IR images of breasts, captured with measuring accuracy of ±0.4% (full scale) and temperature resolution of 0.1 °C black body, depicting malignant, benign and normal pathologies are used in this study. Breast images are registered using their lower boundaries, automatically extracted using landmark points whose locations are learned during training. Boundaries are extracted using Canny edge detection and elimination of inner edges. Breast images are then segmented using fuzzy c-means clustering and the hottest regions are selected for feature extraction. Bispectral invariant features are extracted from Radon projections of these images. An Adaboost classifier is used to select and fuse the best features during training and then classify unseen test images into malignant, benign and normal classes. A data set comprising 9 malignant, 12 benign and 11 normal cases is used for evaluation of performance. Malignant cases are detected with 95% accuracy. A variant of the features using the normalized bispectrum, which discards all magnitude information, is shown to perform better for classification between benign and normal cases, with 83% accuracy compared to 66% for the original.

Scene invariant multi camera crowd counting

Automated crowd counting has become an active field of computer vision research in recent years. Existing approaches are scene-specific, as they are designed to operate in the single camera viewpoint that was used to train the system. Real world camera networks often span multiple viewpoints within a facility, including many regions of overlap. This paper proposes a novel scene invariant crowd counting algorithm that is designed to operate across multiple cameras. The approach uses camera calibration to normalise features between viewpoints and to compensate for regions of overlap. This compensation is performed by constructing an 'overlap map' which provides a measure of how much an object at one location is visible within other viewpoints. An investigation into the suitability of various feature types and regression models for scene invariant crowd counting is also conducted. The features investigated include object size, shape, edges and keypoints. The regression models evaluated include neural networks, K-nearest neighbours, linear and Gaussian process regresion. Our experiments demonstrate that accurate crowd counting was achieved across seven benchmark datasets, with optimal performance observed when all features were used and when Gaussian process regression was used. The combination of scene invariance and multi camera crowd counting is evaluated by training the system on footage obtained from the QUT camera network and testing it on three cameras from the PETS 2009 database. Highly accurate crowd counting was observed with a mean relative error of less than 10%. Our approach enables a pre-trained system to be deployed on a new environment without any additional training, bringing the field one step closer toward a 'plug and play' system.

Towards condition-invariant, top-down visual place recognition

In this paper we present a novel place recognition algorithm inspired by recent discoveries in human visual neuroscience. The algorithm combines intolerant but fast low resolution whole image matching with highly tolerant, sub-image patch matching processes. The approach does not require prior training and works on single images (although we use a cohort normalization score to exploit temporal frame information), alleviating the need for either a velocity signal or image sequence, differentiating it from current state of the art methods. We demonstrate the algorithm on the challenging Alderley sunny day – rainy night dataset, which has only been previously solved by integrating over 320 frame long image sequences. The system is able to achieve 21.24% recall at 100% precision, matching drastically different day and night-time images of places while successfully rejecting match hypotheses between highly aliased images of different places. The results provide a new benchmark for single image, condition-invariant place recognition.

Lighting invariant urban street classification

In this paper we propose the hybrid use of illuminant invariant and RGB images to perform image classification of urban scenes despite challenging variation in lighting conditions. Coping with lighting change (and the shadows thereby invoked) is a non-negotiable requirement for long term autonomy using vision. One aspect of this is the ability to reliably classify scene components in the presence of marked and often sudden changes in lighting. This is the focus of this paper. Posed with the task of classifying all parts in a scene from a full colour image, we propose that lighting invariant transforms can reduce the variability of the scene, resulting in a more reliable classification. We leverage the ideas of “data transfer” for classification, beginning with full colour images for obtaining candidate scene-level matches using global image descriptors. This is commonly followed by superpixellevel matching with local features. However, we show that if the RGB images are subjected to an illuminant invariant transform before computing the superpixel-level features, classification is significantly more robust to scene illumination effects. The approach is evaluated using three datasets. The first being our own dataset and the second being the KITTI dataset using manually generated ground truth for quantitative analysis. We qualitatively evaluate the method on a third custom dataset over a 750m trajectory.

Towards Vision-Based Pose- and Condition-Invariant Place Recognition along Routes

Vision-based place recognition involves recognising familiar places despite changes in environmental conditions or camera viewpoint (pose). Existing training-free methods exhibit excellent invariance to either of these challenges, but not both simultaneously. In this paper, we present a technique for condition-invariant place recognition across large lateral platform pose variance for vehicles or robots travelling along routes. Our approach combines sideways facing cameras with a new multi-scale image comparison technique that generates synthetic views for input into the condition-invariant Sequence Matching Across Route Traversals (SMART) algorithm. We evaluate the system’s performance on multi-lane roads in two different environments across day-night cycles. In the extreme case of day-night place recognition across the entire width of a four-lane-plus-median-strip highway, we demonstrate performance of up to 44% recall at 100% precision, where current state-of-the-art fails.

Unsupervised online learning of condition-invariant images for place recognition

This paper presents an online, unsupervised training algorithm enabling vision-based place recognition across a wide range of changing environmental conditions such as those caused by weather, seasons, and day-night cycles. The technique applies principal component analysis to distinguish between aspects of a location’s appearance that are condition-dependent and those that are condition-invariant. Removing the dimensions associated with environmental conditions produces condition-invariant images that can be used by appearance-based place recognition methods. This approach has a unique benefit – it requires training images from only one type of environmental condition, unlike existing data-driven methods that require training images with labelled frame correspondences from two or more environmental conditions. The method is applied to two benchmark variable condition datasets. Performance is equivalent or superior to the current state of the art despite the lesser training requirements, and is demonstrated to generalise to previously unseen locations.

Dataset-invariant covariance normalization for out-domain PLDA speaker verification

In this paper we introduce a novel domain-invariant covariance normalization (DICN) technique to relocate both in-domain and out-domain i-vectors into a third dataset-invariant space, providing an improvement for out-domain PLDA speaker verification with a very small number of unlabelled in-domain adaptation i-vectors. By capturing the dataset variance from a global mean using both development out-domain i-vectors and limited unlabelled in-domain i-vectors, we could obtain domain- invariant representations of PLDA training data. The DICN- compensated out-domain PLDA system is shown to perform as well as in-domain PLDA training with as few as 500 unlabelled in-domain i-vectors for NIST-2010 SRE and 2000 unlabelled in-domain i-vectors for NIST-2008 SRE, and considerable relative improvement over both out-domain and in-domain PLDA development if more are available.

A frame-invariant scheme for the geometrically exact beam using rotation vector parametrization

While frame-invariant solutions for arbitrarily large rotational deformations have been reported through the orthogonal matrix parametrization, derivation of such solutions purely through a rotation vector parametrization, which uses only three parameters and provides a parsimonious storage of rotations, is novel and constitutes the subject of this paper. In particular, we employ interpolations of relative rotations and a new rotation vector update for a strain-objective finite element formulation in the material framework. We show that the update provides either the desired rotation vector or its complement. This rules out an additive interpolation of total rotation vectors at the nodes. Hence, interpolations of relative rotation vectors are used. Through numerical examples, we show that combining the proposed update with interpolations of relative rotations yields frame-invariant and path-independent numerical solutions. Advantages of the present approach vis-a-vis the updated Lagrangian formulation are also analyzed.