Electron tomography at 2.4 {\AA} resolution

Transmission electron microscopy (TEM) is a powerful imaging tool that has found broad application in materials science, nanoscience and biology(1-3). With the introduction of aberration-corrected electron lenses, both the spatial resolution and image quality in TEM have been significantly improved(4,5) and resolution below 0.5 {\AA} has been demonstrated(6). To reveal the 3D structure of thin samples, electron tomography is the method of choice(7-11), with resolutions of ~1 nm^3 currently achievable(10,11). Recently, discrete tomography has been used to generate a 3D atomic reconstruction of a silver nanoparticle 2-3 nm in diameter(12), but this statistical method assumes prior knowledge of the particle's lattice structure and requires that the atoms fit rigidly on that lattice. Here we report the experimental demonstration of a general electron tomography method that achieves atomic scale resolution without initial assumptions about the sample structure. By combining a novel projection alignment and tomographic reconstruction method with scanning transmission electron microscopy, we have determined the 3D structure of a ~10 nm gold nanoparticle at 2.4 {\AA} resolution. While we cannot definitively locate all of the atoms inside the nanoparticle, individual atoms are observed in some regions of the particle and several grains are identified at three dimensions. The 3D surface morphology and internal lattice structure revealed are consistent with a distorted icosahedral multiply-twinned particle. We anticipate that this general method can be applied not only to determine the 3D structure of nanomaterials at atomic scale resolution(13-15), but also to improve the spatial resolution and image quality in other tomography fields(7,9,16-20).Comment: 27 pages, 17 figure

Shape-based invariant features extraction for object recognition

International audienceThe emergence of new technologies enables generating large quantity of digital information including images; this leads to an increasing number of generated digital images. Therefore it appears a necessity for automatic systems for image retrieval. These systems consist of techniques used for query specification and re-trieval of images from an image collection. The most frequent and the most com-mon means for image retrieval is the indexing using textual keywords. But for some special application domains and face to the huge quantity of images, key-words are no more sufficient or unpractical. Moreover, images are rich in content; so in order to overcome these mentioned difficulties, some approaches are pro-posed based on visual features derived directly from the content of the image: these are the content-based image retrieval (CBIR) approaches. They allow users to search the desired image by specifying image queries: a query can be an exam-ple, a sketch or visual features (e.g., colour, texture and shape). Once the features have been defined and extracted, the retrieval becomes a task of measuring simi-larity between image features. An important property of these features is to be in-variant under various deformations that the observed image could undergo. In this chapter, we will present a number of existing methods for CBIR applica-tions. We will also describe some measures that are usually used for similarity measurement. At the end, and as an application example, we present a specific ap-proach, that we are developing, to illustrate the topic by providing experimental results

Shape analysis and description based on the isometric invariances of topological skeletonization

ilustracionesIn this dissertation, we explore the problem of how to describe the shape of an object in 2D and 3D with a set of features that are invariant to isometric transformations. We focus to based our approach on the well-known Medial Axis Transform and its topological properties. We aim to study two problems. The first is how to find a shape representation of a segmented object that exhibits rotation, translation, and reflection invariance. The second problem is how to build a machine learning pipeline that uses the isometric invariance of the shape representation to do both classification and retrieval. Our proposed solution demonstrates competitive results compared to state-of-the-art approaches. We based our shape representation on the medial axis transform (MAT), sometimes called the topological skeleton. Accepted and well-studied properties of the medial axis include: homotopy preservation, rotation invariance, mediality, one pixel thickness, and the ability to fully reconstruct the object. These properties make the MAT a suitable input to create shape features; however, several problems arise because not all skeletonization methods satisfy all the above-mentioned properties at the same time. In general, skeletons based on thinning approaches preserve topology but are noise sensitive and do not allow a proper reconstruction. They are also not invariant to rotations. Voronoi skeletons also preserve topology and are rotation invariant, but do not have information about the thickness of the object, making reconstruction impossible. The Voronoi skeleton is an approximation of the real skeleton. The denser the sampling of the boundary, the better the approximation; however, a denser sampling makes the Voronoi diagram more computationally expensive. In contrast, distance transform methods allow the reconstruction of the original object by providing the distance from every pixel in the skeleton to the boundary. Moreover, they exhibit an acceptable degree of the properties listed above, but noise sensitivity remains an issue. Therefore, we selected distance transform medial axis methods as our skeletonization strategy, and focused on creating a new noise-free approach to solve the contour noise problem. To effectively classify an object, or perform any other task with features based on its shape, the descriptor needs to be a normalized, compact form: $\Phi$ should map every shape $\Omega$ to the same vector space $\mathrm{R}^{n}$. This is not possible with skeletonization methods because the skeletons of different objects have different numbers of branches and different numbers of points, even when they belong to the same category. Consequently, we developed a strategy to extract features from the skeleton through the map $\Phi$, which we used as an input to a machine learning approach. After developing our method for robust skeletonization, the next step is to use such skeleton into the machine learning pipeline to classify object into previously defined categories. We developed a set of skeletal features that were used as input data to the machine learning architectures. We ran experiments on MPEG7 and ModelNet40 dataset to test our approach in both 2D and 3D. Our experiments show results comparable with the state-of-the-art in shape classification and retrieval. Our experiments also show that our pipeline and our skeletal features exhibit some degree of invariance to isometric transformations. In this study, we sought to design an isometric invariant shape descriptor through robust skeletonization enforced by a feature extraction pipeline that exploits such invariance through a machine learning methodology. We conducted a set of classification and retrieval experiments over well-known benchmarks to validate our proposed method. (Tomado de la fuente)En esta disertación se explora el problema de cómo describir la forma de un objeto en 2D y 3D con un conjunto de características que sean invariantes a transformaciones isométricas. La metodología propuesta en este documento se enfoca en la Transformada del Eje Medio (Medial Axis Transform) y sus propiedades topológicas. Nuestro objetivo es estudiar dos problemas. El primero es encontrar una representación matemática de la forma de un objeto que exhiba invarianza a las operaciones de rotación, translación y reflexión. El segundo problema es como construir un modelo de machine learning que use esas invarianzas para las tareas de clasificación y consulta de objetos a través de su forma. El método propuesto en esta tesis muestra resultados competitivos en comparación con otros métodos del estado del arte. En este trabajo basamos nuestra representación de forma en la transformada del eje medio, a veces llamada esqueleto topológico. Algunas propiedades conocidas y bien estudiadas de la transformada del eje medio son: conservación de la homotopía, invarianza a la rotación, su grosor consiste en un solo pixel (1D), y la habilidad para reconstruir el objeto original a través de ella. Estas propiedades hacen de la transformada del eje medio un punto de partida adecuado para crear características de forma. Sin embargo, en este punto surgen varios problemas dado que no todos los métodos de esqueletización satisfacen, al mismo tiempo, todas las propiedades mencionadas anteriormente. En general, los esqueletos basados en enfoques de erosión morfológica conservan la topología del objeto, pero son sensibles al ruido y no permiten una reconstrucción adecuada. Además, no son invariantes a las rotaciones. Otro método de esqueletización son los esqueletos de Voronoi. Los esqueletos de Voronoi también conservan la topología y son invariantes a la rotación, pero no tienen información sobre el grosor del objeto, lo que hace imposible su reconstrucción. Cuanto más denso sea el muestreo del contorno del objeto, mejor será la aproximación. Sin embargo, un muestreo más denso hace que el diagrama de Voronoi sea más costoso computacionalmente. Por el contrario, los métodos basados en la transformada de la distancia permiten la reconstrucción del objeto original, ya que proporcionan la distancia desde cada píxel del esqueleto hasta su punto más cercano en el contorno. Además, exhiben un grado aceptable de las propiedades enumeradas anteriormente, aunque la sensibilidad al ruido sigue siendo un problema. Por lo tanto, en este documento seleccionamos los métodos basados en la transformada de la distancia como nuestra estrategia de esqueletización, y nos enfocamos en crear un nuevo enfoque que resuelva el problema del ruido en el contorno. Para clasificar eficazmente un objeto o realizar cualquier otra tarea con características basadas en su forma, el descriptor debe ser compacto y estar normalizado: $\Phi$ debe relacionar cada forma $\Omega$ al mismo espacio vectorial $\mathrm{R}^{n}$. Esto no es posible con los métodos de esqueletización en el estado del arte, porque los esqueletos de diferentes objetos tienen diferentes números de ramas y diferentes números de puntos incluso cuando pertenecen a la misma categoría. Consecuentemente, en nuestra propuesta desarrollamos una estrategia para extraer características del esqueleto a través de la función $\Phi$, que usamos como entrada para un enfoque de aprendizaje automático. % TODO completar con resultados. Después de desarrollar nuestro método de esqueletización robusta, el siguiente paso es usar dicho esqueleto en un modelo de aprendizaje de máquina para clasificar el objeto en categorías previamente definidas. Para ello se desarrolló un conjunto de características basadas en el eje medio que se utilizaron como datos de entrada para la arquitectura de aprendizaje automático. Realizamos experimentos en los conjuntos de datos: MPEG7 y ModelNet40 para probar nuestro enfoque tanto en 2D como en 3D. Nuestros experimentos muestran resultados comparables con el estado del arte en clasificación y consulta de formas (retrieval). Nuestros experimentos también muestran que el modelo desarrollado junto con nuestras características basadas en el eje medio son invariantes a las transformaciones isométricas. (Tomado de la fuente)Beca para Doctorados Nacionales de Colciencias, convocatoria 725 de 2015DoctoradoDoctor en IngenieríaVisión por computadora y aprendizaje automátic

Robust and efficient Fourier-Mellin transform approximations for invariant grey-level image description and reconstruction

International audienceThis paper addresses the gray-level image representation ability of the Fourier-Mellin Transform (FMT) for pattern recognition, reconstruction and image database retrieval. The main practical di±culty of the FMT lies in the accuracy and e±ciency of its numerical approximation and we propose three estimations of its analytical extension. Comparison of these approximations is performed from discrete and ¯nite-extent sets of Fourier- Mellin harmonics by means of experiments in: (i) image reconstruction via both visual inspection and the computation of a reconstruction error; and (ii) pattern recognition and discrimination by using a complete and convergent set of features invariant under planar similarities. Experimental results on real gray-level images show that it is possible to recover an image to within a speci¯ed degree of accuracy and to classify objects reliably even when a large set of descriptors is used. Finally, an example will be given, illustrating both theoretical and numerical results in the context of content-based image retrieval