An Optical Flow Based Left-Invariant Metric for Natural Gradient Descent in Affine Image Registration

Accurate spatial alignment is essential for any population neuroimaging study, and affine (12 parameter linear/translation) or rigid (6 parameter rotation/translation) alignments play a major role. Here we consider intensity based alignment of neuroimages using gradient based optimization, which is a problem that continues to be important in many other areas of medical imaging and computer vision in general. A key challenge is robustness. Optimization often fails when transformations have components with different characteristic scales, such as linear versus translation parameters. Hand tuning or other scaling approaches have been used, but efficient automatic methods are essential for generalizing to new imaging modalities, to specimens of different sizes, and to big datasets where manual approaches are not feasible. To address this we develop a left invariant metric on these two matrix groups, based on the norm squared of optical flow induced on a template image. This metric is used in a natural gradient descent algorithm, where gradients (covectors) are converted to perturbations (vectors) by applying the inverse of the metric to define a search direction in which to update parameters. Using a publicly available magnetic resonance neuroimage database, we show that this approach outperforms several other gradient descent optimization strategies. Due to left invariance, our metric needs to only be computed once during optimization, and can therefore be implemented with negligible computation time.

Optimal affine image normalization approach for optical character recognition

Optical character recognition (OCR) in images captured from arbitrary angles requires preliminary normalization, i.e. a geometric transformation resulting in an image as if it was captured at an angle suitable for OCR. In most cases, a surface containing characters can be considered flat, and a pinhole model can be adopted for a camera. Thus, in theory, the normalization should be projective. Usually, the camera optical axis is approximately perpendicular to the document surface, so the projective normalization can be replaced with an affine one without a significant loss of accuracy. An affine image transformation is performed significantly faster than a projective normalization, which is important for OCR on mobile devices. In this work, we propose a fast approach for image normalization. It utilizes an affine normalization instead of a projective one if there is no significant loss of accuracy. The approach is based on a proposed criterion for the normalization accuracy: root mean square (RMS) coordinate discrepancies over the region of interest (ROI). The problem of optimal affine normalization according to this criterion is considered. We have established that this unconstrained optimization is quadratic and can be reduced to a problem of fractional quadratic functions integration over the ROI. The latter was solved analytically in the case of OCR where the ROI consists of rectangles. The proposed approach is generalized for various cases when instead of the affine transform its special cases are used: scaling, translation, shearing, and their superposition, allowing the image normalization procedure to be further accelerated.

On the Affine Image of a Rational Surface of Revolution

We study the properties of the image of a rational surface of revolution under a nonsingular affine mapping. We prove that this image has a notable property, namely that all the affine normal lines, a concept that appears in the context of affine differential geometry, created by Blaschke in the first decades of the 20th century, intersect a fixed line. Given a rational surface with this property, which can be algorithmically checked, we provide an algorithmic method to find a surface of revolution, if it exists, whose image under an affine mapping is the given surface; the algorithm also finds the affine transformation mapping one surface onto the other. Finally, we also prove that the only rational affine surfaces of rotation, a generalization of surfaces of revolution that arises in the context of affine differential geometry, and which includes surfaces of revolution as a subtype, affinely transforming into a surface of revolution are the surfaces of revolution, and that in that case the affine mapping must be a similarity.

Hybrid Malware Classification Method Using Segmentation-Based Fractal Texture Analysis and Deep Convolution Neural Network Features

As the number of internet users increases so does the number of malicious attacks using malware. The detection of malicious code is becoming critical, and the existing approaches need to be improved. Here, we propose a feature fusion method to combine the features extracted from pre-trained AlexNet and Inception-v3 deep neural networks with features attained using segmentation-based fractal texture analysis (SFTA) of images representing the malware code. In this work, we use distinctive pre-trained models (AlexNet and Inception-V3) for feature extraction. The purpose of deep convolutional neural network (CNN) feature extraction from two models is to improve the malware classifier accuracy, because both models have characteristics and qualities to extract different features. This technique produces a fusion of features to build a multimodal representation of malicious code that can be used to classify the grayscale images, separating the malware into 25 malware classes. The features that are extracted from malware images are then classified using different variants of support vector machine (SVM), k-nearest neighbor (KNN), decision tree (DT), and other classifiers. To improve the classification results, we also adopted data augmentation based on affine image transforms. The presented method is evaluated on a Malimg malware image dataset, achieving an accuracy of 99.3%, which makes it the best among the competing approaches.

Steiner's Hat: a Constant-Area Deltoid Associated with the Ellipse

The Negative Pedal Curve (NPC) of the Ellipse with respect to a boundary point M is a 3-cusp closed-curve which is the affine image of the Steiner Deltoid. Over all M the family has invariant area and displays an array of interesting properties.

Affine registration of multispectral images of historical documents for optimized feature recovery

Multispectral (MSI) imaging of historical documents can recover lost features, such as text or drawings. This technique involves capturing multiple images of a document illuminated using different wavelengths of light. The images created must be registered in order to ensure optimal results are produced from any subsequent image processing techniques. However, the images may be misaligned due to the presence of optical elements such as filters, or because they were acquired at different times or because the images were captured from different copies of the documents . There is little prior work or information available about which image registration techniques are most appropriate. Image registration of multispectral images is challenging as the illumination changes for each image and the features visible in images captured at different wavelengths may not appear consistently throughout the image sequence. Here, we compare three image registration techniques: two based on similarity measures and a method based on phase correlation. These methods are characterized by applying them to realistic surrogate images and then assessed on three different sets of real multispectral images. Mutual information is recommended as a measure for affine image registration when working with multispectral images of documentary material as it was proven to be more robust than the other techniques tested.