Affine Geometric Transformations Research Articles

Detecting Infected Cucumber Plants with Close-Range Multispectral Imagery

This study used close-range multispectral imagery over cucumber plants inside a commercial greenhouse to detect powdery mildew due to Podosphaera xanthii. It was collected using a MicaSense® RedEdge camera at 1.5 m over the top of the plant. Image registration was performed using Speeded-Up Robust Features (SURF) with an affine geometric transformation. The image background was removed using a binary mask created with the aligned NIR band of each image, and the illumination was corrected using Cheng et al.’s algorithm. Different features were computed, including RGB, image reflectance values, and several vegetation indices. For each feature, a fine Gaussian Support Vector Machines algorithm was trained and validated to classify healthy and infected pixels. The data set to train and validate the SVM was composed of 1000 healthy and 1000 infected pixels, split 70–30% into training and validation datasets, respectively. The overall validation accuracy was 89, 73, 82, 51, and 48%, respectively, for blue, green, red, red-edge, and NIR band image. With the RGB images, we obtained an overall validation accuracy of 89%, while the best vegetation index image was the PMVI-2 image which produced an overall accuracy of 81%. Using the five bands together, overall accuracy dropped from 99% in the training to 57% in the validation dataset. While the results of this work are promising, further research should be considered to increase the number of images to achieve better training and validation datasets.

Nanoindentation in multi-modal map combinations: a correlative approach to local mechanical property assessment

A method is presented for the registration and correlation of property maps of materials, including data from nanoindentation hardness, Electron Back-Scattered Diffraction (EBSD), and Electron Micro-Probe Analysis (EPMA). This highly spatially resolved method allows for the study of micron-scale microstructural features, and has the capability to rapidly extract correlations between multiple features of interest from datasets containing thousands of data points. Two case studies are presented in commercially pure (CP) titanium: in the first instance, the effect of crystal anisotropy on measured hardness and, in the second instance, the effect of an oxygen diffusion layer on hardness. The independently collected property maps are registered using affine geometric transformations and are interpolated to allow for direct correlation. The results show strong agreement with trends observed in the literature, as well as providing a large dataset to facilitate future statistical analysis of microstructure-dependent mechanisms.Graphical abstract

Geometry and Radiometry Invariant Matched Manifold Detection

Consider a set of deformable objects undergoing geometric and radiometric transformations. As a result of the action of these transformations, the set of different realizations of each object is generally a manifold in the space of observations. Assuming the geometric deformations an object undergoes, belong to some finite dimensional family, it has been shown that the universal manifold embedding (UME) provides a set of nonlinear operators that universally maps each of the different manifolds, where each manifold is generated by the set all of possible appearances of a single object, into a distinct linear subspace of an Euclidean space. In this paper, we generalize this framework to the case where the observed object undergoes both an affine geometric transformation, and a monotonic radiometric transformation, and present a novel framework for the detection and recognition of the deformable objects. Applying to each of the observations an operator that makes it invariant to monotonic amplitude transformations, but is geometry-covariant with the affine transformation, the set of all possible observations on that object is mapped by the UME into a single linear subspace-invariant with respect to both the geometric and radiometric transformations. The embedding of the space of observations is independent of the specific observed object; hence it is universal. The invariant representation of the object is the basis of a matched manifold detection and tracking framework of objects that undergo complex geometric and radiometric deformations: the observed surface is tessellated into a set of tiles such that the deformation of each one is well approximated by an affine geometric transformation and a monotonic transformation of the measured intensities. Since each tile is mapped by the radiometry invariant UME to a distinct linear subspace, the detection and tracking problems are solved by evaluating distances between linear subspaces. Classification in this context becomes a problem of determining which labeled subspace in a Grassmannian is closest to a subspace in the same Grassmannian, where the latter has been generated by radiometry invariant UME from an unlabeled observation.

A parametric intensity-based 3D image registration method for magnetic resonance imaging

Image registration (IR) aims to map one image to another of a same scene. With rapid progress in image acquisition technologies, 3D IR becomes an important problem in magnetic resonance imaging (MRI) and other applications. In the literature, however, most IR methods are for 2D images and there are only a limited number of 3D methods available. Because 3D images have much complicated structure than their 2D counterparts, 3D IR is not just a simple generalization of the 2D IR problem. In this paper, we develop a 3D IR method that can handle cases with affine geometric transformations well. By its definition, an affine transformation maps a line to a line, and it includes rotation, translation, and scaling as special cases. In practice, most geometric transformations involved in IR problems are affine transformations. Therefore, our proposed method can find many IR applications. It is shown that this method works well in various cases, including cases when the data size of a 3D image is reduced for different reasons. This latter property makes it attractive for many 3D IR applications, since 3D images are often big in data size and it is natural to reduce their size for fast computation.

Individualised avatars with complete anatomy constructed from the ANSUR II 3-D anthropometric database

Individualised 3-D finite element (FE) mesh static avatars with complete labelled internal anatomy were constructed in a fully computerised fashion using 3-D body surface scan mesh data from the ANSUR II 3-D anthropometric database. A combination of skeleton matching, landmark matching and surface matching were employed in a fully automatic method to generate affine geometric transformations deforming a segmented 3-D FE mesh (i.e., having labelled tetrahedral elements) representing standard genderspecific human anatomy. The standard anatomy was deformed to fit into the FE mesh of an individual's body surface scan acquired in the ANSUR II anthropometric study. Two hundred fifty male avatars were computed.

A Novel Form of Affine Moment Invariants of Grayscale Images

We present a general method to derive robust invariants of grayscale images under affine geometric transformation. In the literature, there are well studied affine moment invariants of grayscale images. The problem is that only few of the invariants are low orders. Higher order affine moment invariants are sensitive to noise and hard to implement. In this paper, we extend the traditional definition of the geometric moment by encapsulating the image functions by some wrapper functions. A general theorem to construct the affine invariants consisting of the extended moments of a grayscale image is presented. Using this method, different forms of low order affine moment invariants are constructed. The traditional affine moment invariants are a special type of the proposed new affine moment invariants. These forms of invariants are less sensitive to noise and easy to implement.DOI: http://dx.doi.org/10.5755/j01.eee.19.1.3262

Combined Affine Geometric Transformations and Spatially Dependent Radiometric Deformations: A Decoupled Linear Estimation Framework

This paper considers the problem of registering two observations of the same object, where the observations differ due to a combined effect of an affine geometric transformation and nonuniform illumination changes. The problem of deriving new representations of the observations that are both invariant to geometric transformations and linear in the illumination model is analyzed. In this framework, we present a novel method for linear estimation of illumination changes in an affine invariant manner, thus, decoupling the original problem into two simpler ones. The computational complexity of the method is low as it requires no more than solving a linear set of equations. The prior step of illumination estimation is shown to improve the accuracy of state-of-the-art registration techniques by a factor of two.

A Compact Representation of Drawing Movements with Sequences of Parabolic Primitives

Some studies suggest that complex arm movements in humans and monkeys may optimize several objective functions, while others claim that arm movements satisfy geometric constraints and are composed of elementary components. However, the ability to unify different constraints has remained an open question. The criterion for a maximally smooth (minimizing jerk) motion is satisfied for parabolic trajectories having constant equi-affine speed, which thus comply with the geometric constraint known as the two-thirds power law. Here we empirically test the hypothesis that parabolic segments provide a compact representation of spontaneous drawing movements. Monkey scribblings performed during a period of practice were recorded. Practiced hand paths could be approximated well by relatively long parabolic segments. Following practice, the orientations and spatial locations of the fitted parabolic segments could be drawn from only 2–4 clusters, and there was less discrepancy between the fitted parabolic segments and the executed paths. This enabled us to show that well-practiced spontaneous scribbling movements can be represented as sequences (“words”) of a small number of elementary parabolic primitives (“letters”). A movement primitive can be defined as a movement entity that cannot be intentionally stopped before its completion. We found that in a well-trained monkey a movement was usually decelerated after receiving a reward, but it stopped only after the completion of a sequence composed of several parabolic segments. Piece-wise parabolic segments can be generated by applying affine geometric transformations to a single parabolic template. Thus, complex movements might be constructed by applying sequences of suitable geometric transformations to a few templates. Our findings therefore suggest that the motor system aims at achieving more parsimonious internal representations through practice, that parabolas serve as geometric primitives and that non-Euclidean variables are employed in internal movement representations (due to the special role of parabolas in equi-affine geometry).

Multiscale Roughness Analysis of Particles: Application to the Classification of Detrital Sediments

The shape of detrital quartz grains, mainly acquired under the effect of mechanical transport agents, has been observed and described for a long time by sedimentologists. The roughness of these grains is recognized as an important parameter for analyzing sediments, but to quantify this parameter with a discriminant measure can be difficult. By using the concept of multiresolution analysis and the wavelet formalism, we develop a roughness descriptor for particles, possessing multiscale analysis capabilities. It allows analyses of wear and erosion phenomena acting on particles by decomposing the information on the shape into different resolution levels, each level corresponding to a different scale. Thus it becomes possible to differentiate coarse roughness from finer roughness of a grain's outline. This descriptor is invariant under affine geometric transformation and can therefore be used to compare sands stemming from a wide range of natural environments. An application to the analysis and the classification of detrital sediments, along with a comparison with Fourier and fractal grain shape analysis, illustrates the performance of the method.

Robust parameterized component analysis: theory and applications to 2D facial appearance models

Principal component analysis (PCA) has been successfully applied to construct linear models of shape, graylevel, and motion in images. In particular, PCA has been widely used to model the variation in the appearance of people’s faces. We extend previous work on facial modeling for tracking faces in video sequences as they undergo significant changes due to facial expressions. Here we consider person-specific facial appearance models (PSFAM), which use modular PCA to model complex intra-person appearance changes. Such models require aligned visual training data; in previous work, this has involved a time consuming and error-prone hand alignment and cropping process. Instead, the main contribution of this paper is to introduce parameterized component analysis to learn a subspace that is invariant to affine (or higher order) geometric transformations. The automatic learning of a PSFAM given a training image sequence is posed as a continuous optimization problem and is solved with a mixture of stochastic and deterministic techniques achieving sub-pixel accuracy. We illustrate the use of the 2D PSFAM model with preliminary experiments relevant to applications including video-conferencing and avatar animation.

Geometric Invariant Shape Representations Using Morphological Multiscale Analysis

In this paper, we present a new geometric invariant shape representation using morphological multiscale analysis. The geometric invariant is based on the area and perimeter evolution of the shape under the action of a morphological multiscale analysis. First, we present some theoretical results on the perimeter and area evolution across the scales of a shape. In the case of similarity transformations, the proposed geometric invariant is based on a scale-normalized evolution of the isoperimetric ratio of the shape. In the case of general affine geometric transformations the proposed geometric invariant is based on a scale-normalized evolution of the area. We present some numerical experiments to evaluate the performance of the proposed models. We present an application of this technique to the problem of shape classification on a real shape database and we study the well-posedness of the proposed models in the framework of viscosity solution theory.

TRASFORM: An Open Environment to Study Affine Geometric Transformations on the Plane

The advantages of an open environment (OE) approach are briefly summarized and an open environment to study the plane affine geometric transformations is described. These transformations play an important role in understanding and learning geometry and key topics in physics and chemistry. TRASFORM's structure is based on a set of correlated functions that can be activated by user‐friendly commands and used in several contexts. The learning path can be completely open or suggested by the teacher according to the planned class activities. The software is supported by an extensive written guide which suggests many problems and exercises and presents hints about some possible pedagogical paths. Up to now, TRASFORM has been used in several teachers’ training courses and in a few ordinary classes with high school students. The qualitative results indicate that the proposed open approach is effective both in stimulating many interactive learning activities and in fostering the use of discovery in the learning/teaching process.