Higher-order regularization and morphological techniques for image segmentation

La segmentación de imágenes es un campo importante de la visión computacional y una de las áreas de investigación más activas, con aplicaciones en comprensión de imágenes, detección de objetos, reconocimiento facial, vigilancia de vídeo o procesamiento de imagen médica. La segmentación de imágenes es un problema difícil en general, pero especialmente en entornos científicos y biomédicos, donde las técnicas de adquisición imagen proporcionan imágenes ruidosas. Además, en muchos de estos casos se necesita una precisión casi perfecta. En esta tesis, revisamos y comparamos primero algunas de las técnicas ampliamente usadas para la segmentación de imágenes médicas. Estas técnicas usan clasificadores a nivel de pixel e introducen regularización sobre pares de píxeles que es normalmente insuficiente. Estudiamos las dificultades que presentan para capturar la información de alto nivel sobre los objetos a segmentar. Esta deficiencia da lugar a detecciones erróneas, bordes irregulares, configuraciones con topología errónea y formas inválidas. Para solucionar estos problemas, proponemos un nuevo método de regularización de alto nivel que aprende información topológica y de forma a partir de los datos de entrenamiento de una forma no paramétrica usando potenciales de orden superior. Los potenciales de orden superior se están popularizando en visión por computador, pero la representación exacta de un potencial de orden superior definido sobre muchas variables es computacionalmente inviable. Usamos una representación compacta de los potenciales basada en un conjunto finito de patrones aprendidos de los datos de entrenamiento que, a su vez, depende de las observaciones. Gracias a esta representación, los potenciales de orden superior pueden ser convertidos a potenciales de orden 2 con algunas variables auxiliares añadidas. Experimentos con imágenes reales y sintéticas confirman que nuestro modelo soluciona los errores de aproximaciones más débiles. Incluso con una regularización de alto nivel, una precisión exacta es inalcanzable, y se requeire de edición manual de los resultados de la segmentación automática. La edición manual es tediosa y pesada, y cualquier herramienta de ayuda es muy apreciada. Estas herramientas necesitan ser precisas, pero también lo suficientemente rápidas para ser usadas de forma interactiva. Los contornos activos son una buena solución: son buenos para detecciones precisas de fronteras y, en lugar de buscar una solución global, proporcionan un ajuste fino a resultados que ya existían previamente. Sin embargo, requieren una representación implícita que les permita trabajar con cambios topológicos del contorno, y esto da lugar a ecuaciones en derivadas parciales (EDP) que son costosas de resolver computacionalmente y pueden presentar problemas de estabilidad numérica. Presentamos una aproximación morfológica a la evolución de contornos basada en un nuevo operador morfológico de curvatura que es válido para superficies de cualquier dimensión. Aproximamos la solución numérica de la EDP de la evolución de contorno mediante la aplicación sucesiva de un conjunto de operadores morfológicos aplicados sobre una función de conjuntos de nivel. Estos operadores son muy rápidos, no sufren de problemas de estabilidad numérica y no degradan la función de los conjuntos de nivel, de modo que no hay necesidad de reinicializarlo. Además, su implementación es mucho más sencilla que la de las EDP, ya que no requieren usar sofisticados algoritmos numéricos. Desde un punto de vista teórico, profundizamos en las conexiones entre operadores morfológicos y diferenciales, e introducimos nuevos resultados en este área. Validamos nuestra aproximación proporcionando una implementación morfológica de los contornos geodésicos activos, los contornos activos sin bordes, y los turbopíxeles. En los experimentos realizados, las implementaciones morfológicas convergen a soluciones equivalentes a aquéllas logradas mediante soluciones numéricas tradicionales, pero con ganancias significativas en simplicidad, velocidad y estabilidad. ABSTRACT Image segmentation is an important field in computer vision and one of its most active research areas, with applications in image understanding, object detection, face recognition, video surveillance or medical image processing. Image segmentation is a challenging problem in general, but especially in the biological and medical image fields, where the imaging techniques usually produce cluttered and noisy images and near-perfect accuracy is required in many cases. In this thesis we first review and compare some standard techniques widely used for medical image segmentation. These techniques use pixel-wise classifiers and introduce weak pairwise regularization which is insufficient in many cases. We study their difficulties to capture high-level structural information about the objects to segment. This deficiency leads to many erroneous detections, ragged boundaries, incorrect topological configurations and wrong shapes. To deal with these problems, we propose a new regularization method that learns shape and topological information from training data in a nonparametric way using high-order potentials. High-order potentials are becoming increasingly popular in computer vision. However, the exact representation of a general higher order potential defined over many variables is computationally infeasible. We use a compact representation of the potentials based on a finite set of patterns learned fromtraining data that, in turn, depends on the observations. Thanks to this representation, high-order potentials can be converted into pairwise potentials with some added auxiliary variables and minimized with tree-reweighted message passing (TRW) and belief propagation (BP) techniques. Both synthetic and real experiments confirm that our model fixes the errors of weaker approaches. Even with high-level regularization, perfect accuracy is still unattainable, and human editing of the segmentation results is necessary. The manual edition is tedious and cumbersome, and tools that assist the user are greatly appreciated. These tools need to be precise, but also fast enough to be used in real-time. Active contours are a good solution: they are good for precise boundary detection and, instead of finding a global solution, they provide a fine tuning to previously existing results. However, they require an implicit representation to deal with topological changes of the contour, and this leads to PDEs that are computationally costly to solve and may present numerical stability issues. We present a morphological approach to contour evolution based on a new curvature morphological operator valid for surfaces of any dimension. We approximate the numerical solution of the contour evolution PDE by the successive application of a set of morphological operators defined on a binary level-set. These operators are very fast, do not suffer numerical stability issues, and do not degrade the level set function, so there is no need to reinitialize it. Moreover, their implementation is much easier than their PDE counterpart, since they do not require the use of sophisticated numerical algorithms. From a theoretical point of view, we delve into the connections between differential andmorphological operators, and introduce novel results in this area. We validate the approach providing amorphological implementation of the geodesic active contours, the active contours without borders, and turbopixels. In the experiments conducted, the morphological implementations converge to solutions equivalent to those achieved by traditional numerical solutions, but with significant gains in simplicity, speed, and stability.

How network operators can enhance ambient assisted living applications through next generation networks

Within the technological framework of Information and Communication Technologies (ICT), consumers are currently requesting multimedia services with simplicity of use, reliability, security and service availability through mobile and fixed access. Network operators are proposing the Next Generation Networks (NGN) to address the challenges of providing both services and network convergence. Apart from these considerations, there is a need to provide social and healthcare assistance services in order to support the progressive aging in the elderly population. In order to achieve this objective, the Ambient Assisted Living (AAL) initiative proposes ICT systems and services to promote autonomy and an independent life among the elderly. This paper describes the design and implementation of a group of services, called “service enablers”, which helps AAL applications to be supported in NGN. The presented enablers are identified to support the teleconsulting applications requirements in an NGN environment, involving the implementation of a virtual waiting room, a virtual whiteboard, a multimedia multiconference and a vital-signs monitoring presence status. A use case is defined and implemented to evaluate the developed enablers' performance.

A Compact Formula for the Derivative of a 3-D Rotation in Exponential Coordinates

We present a compact formula for the derivative of a 3-D rotation matrix with respect to its exponential coordinates. A geometric interpretation of the resulting expression is provided, as well as its agreement with other less-compact but better-known formulas. To the best of our knowledge, this simpler formula does not appear anywhere in the literature. We hope by providing this more compact expression to alleviate the common pressure to reluctantly resort to alternative representations in various computational applications simply as a means to avoid the complexity of differential analysis in exponential coordinates.

A genetic algorithm for slope stability analyses with concave slip surfaces using custom operators

Heuristic methods are popular tools to find critical slip surfaces in slope stability analyses. A new genetic algorithm (GA) is proposed in this work that has a standard structure but a novel encoding and generation of individuals with custom-designed operators for mutation and crossover that produce kinematically feasible slip surfaces with a high probability. In addition, new indices to assess the efficiency of operators in their search for the minimum factor of safety (FS) are proposed. The proposed GA is applied to traditional benchmark examples from the literature, as well as to a new practical example. Results show that the proposed GA is reliable, flexible and robust: it provides good minimum FS estimates that are not very sensitive to the number of nodes and that are very similar for different replications

Compact duplexing for a 680-GHz radar using a waveguide orthomode transducer

A compact 680-GHz waveguide orthomode transducer (OMT) and circular horn combination has been designed, tested, and characterized in a radar transceiver's duplexer. The duplexing capability is implemented by a hybrid waveguide quasi optical solution, combining a linear polarization OMT and an external grating polarizer. Isolation between the OMT's orthogonal ports' flanges was measured with a vector network analyzer to exceed 33 dB over a >10% bandwidth between 630 and 710 GHz. Calibrated Y-factor measurements using a mixer attached to the OMT ports reveal losses through the transmit and receive paths that sum to an average of 4.7 dB of two-way loss over 660-690 GHz. This is consistent with radar sensitivity measurements comparing the new OMT/horn with a quasi-optical wire grid beam splitter. Moreover, the radar performance assessment validates the OMT as a suitable compact substitute of the wire grid for the JPL's short-range 680-GHz imaging radar.

Design and development of compact optical systems = Diseño y desarrollo de sistemas ópticos compactos

Esta tesis considera dos tipos de aplicaciones del diseño óptico: óptica formadora de imagen por un lado, y óptica anidólica (nonimaging) o no formadora de imagen, por otro. Las ópticas formadoras de imagen tienen como objetivo la obtención de imágenes de puntos del objeto en el plano de la imagen. Por su parte, la óptica anidólica, surgida del desarrollo de aplicaciones de concentración e iluminación, se centra en la transferencia de energía en forma de luz de forma eficiente. En general, son preferibles los diseños ópticos que den como resultado sistemas compactos, para ambos tipos de ópticas (formadora de imagen y anidólica). En el caso de los sistemas anidólicos, una óptica compacta permite tener costes de producción reducidos. Hay dos razones: (1) una óptica compacta presenta volúmenes reducidos, lo que significa que se necesita menos material para la producción en masa; (2) una óptica compacta es pequeña y ligera, lo que ahorra costes en el transporte. Para los sistemas ópticos de formación de imagen, además de las ventajas anteriores, una óptica compacta aumenta la portabilidad de los dispositivos, que es una gran ventaja en tecnologías de visualización portátiles, tales como cascos de realidad virtual (HMD del inglés Head Mounted Display). Esta tesis se centra por tanto en nuevos enfoques de diseño de sistemas ópticos compactos para aplicaciones tanto de formación de imagen, como anidólicas. Los colimadores son uno de los diseños clásicos dentro la óptica anidólica, y se pueden utilizar en aplicaciones fotovoltaicas y de iluminación. Hay varios enfoques a la hora de diseñar estos colimadores. Los diseños convencionales tienen una relación de aspecto mayor que 0.5. Con el fin de reducir la altura del colimador manteniendo el área de iluminación, esta tesis presenta un diseño de un colimador multicanal. En óptica formadora de imagen, las superficies asféricas y las superficies sin simetría de revolución (o freeform) son de gran utilidad de cara al control de las aberraciones de la imagen y para reducir el número y tamaño de los elementos ópticos. Debido al rápido desarrollo de sistemas de computación digital, los trazados de rayos se pueden realizar de forma rápida y sencilla para evaluar el rendimiento del sistema óptico analizado. Esto ha llevado a los diseños ópticos modernos a ser generados mediante el uso de diferentes técnicas de optimización multi-paramétricas. Estas técnicas requieren un buen diseño inicial como punto de partida para el diseño final, que será obtenido tras un proceso de optimización. Este proceso precisa un método de diseño directo para superficies asféricas y freeform que den como resultado un diseño cercano al óptimo. Un método de diseño basado en ecuaciones diferenciales se presenta en esta tesis para obtener un diseño óptico formado por una superficie freeform y dos superficies asféricas. Esta tesis consta de cinco capítulos. En Capítulo 1, se presentan los conceptos básicos de la óptica formadora de imagen y de la óptica anidólica, y se introducen las técnicas clásicas del diseño de las mismas. El Capítulo 2 describe el diseño de un colimador ultra-compacto. La relación de aspecto ultra-baja de este colimador se logra mediante el uso de una estructura multicanal. Se presentará su procedimiento de diseño, así como un prototipo fabricado y la caracterización del mismo. El Capítulo 3 describe los conceptos principales de la optimización de los sistemas ópticos: función de mérito y método de mínimos cuadrados amortiguados. La importancia de un buen punto de partida se demuestra mediante la presentación de un mismo ejemplo visto a través de diferentes enfoques de diseño. El método de las ecuaciones diferenciales se presenta como una herramienta ideal para obtener un buen punto de partida para la solución final. Además, diferentes técnicas de interpolación y representación de superficies asféricas y freeform se presentan para el procedimiento de optimización. El Capítulo 4 describe la aplicación del método de las ecuaciones diferenciales para un diseño de un sistema óptico de una sola superficie freeform. Algunos conceptos básicos de geometría diferencial son presentados para una mejor comprensión de la derivación de las ecuaciones diferenciales parciales. También se presenta un procedimiento de solución numérica. La condición inicial está elegida como un grado de libertad adicional para controlar la superficie donde se forma la imagen. Basado en este enfoque, un diseño anastigmático se puede obtener fácilmente y se utiliza como punto de partida para un ejemplo de diseño de un HMD con una única superficie reflectante. Después de la optimización, dicho diseño muestra mejor rendimiento. El Capítulo 5 describe el método de las ecuaciones diferenciales ampliado para diseños de dos superficies asféricas. Para diseños ópticos de una superficie, ni la superficie de imagen ni la correspondencia entre puntos del objeto y la imagen pueden ser prescritas. Con esta superficie adicional, la superficie de la imagen se puede prescribir. Esto conduce a un conjunto de tres ecuaciones diferenciales ordinarias implícitas. La solución numérica se puede obtener a través de cualquier software de cálculo numérico. Dicho procedimiento también se explica en este capítulo. Este método de diseño da como resultado una lente anastigmática, que se comparará con una lente aplanática. El diseño anastigmático converge mucho más rápido en la optimización y la solución final muestra un mejor rendimiento. ABSTRACT We will consider optical design from two points of view: imaging optics and nonimaging optics. Imaging optics focuses on the imaging of the points of the object. Nonimaging optics arose from the development of concentrators and illuminators, focuses on the transfer of light energy, and has wide applications in illumination and concentration photovoltaics. In general, compact optical systems are necessary for both imaging and nonimaging designs. For nonimaging optical systems, compact optics use to be important for reducing cost. The reasons are twofold: (1) compact optics is small in volume, which means less material is needed for mass-production; (2) compact optics is small in size and light in weight, which saves cost in transportation. For imaging optical systems, in addition to the above advantages, compact optics increases portability of devices as well, which contributes a lot to wearable display technologies such as Head Mounted Displays (HMD). This thesis presents novel design approaches of compact optical systems for both imaging and nonimaging applications. Collimator is a typical application of nonimaging optics in illumination, and can be used in concentration photovoltaics as well due to the reciprocity of light. There are several approaches for collimator designs. In general, all of these approaches have an aperture diameter to collimator height not greater than 2. In order to reduce the height of the collimator while maintaining the illumination area, a multichannel design is presented in this thesis. In imaging optics, aspheric and freeform surfaces are useful in controlling image aberrations and reducing the number and size of optical elements. Due to the rapid development of digital computing systems, ray tracing can be easily performed to evaluate the performance of optical system. This has led to the modern optical designs created by using different multi-parametric optimization techniques. These techniques require a good initial design to be a starting point so that the final design after optimization procedure can reach the optimum solution. This requires a direct design method for aspheric and freeform surface close to the optimum. A differential equation based design method is presented in this thesis to obtain single freeform and double aspheric surfaces. The thesis comprises of five chapters. In Chapter 1, basic concepts of imaging and nonimaging optics are presented and typical design techniques are introduced. Readers can obtain an understanding for the following chapters. Chapter 2 describes the design of ultra-compact collimator. The ultra-low aspect ratio of this collimator is achieved by using a multichannel structure. Its design procedure is presented together with a prototype and its evaluation. The ultra-compactness of the device has been approved. Chapter 3 describes the main concepts of optimizing optical systems: merit function and Damped Least-Squares method. The importance of a good starting point is demonstrated by presenting an example through different design approaches. The differential equation method is introduced as an ideal tool to obtain a good starting point for the final solution. Additionally, different interpolation and representation techniques for aspheric and freeform surface are presented for optimization procedure. Chapter 4 describes the application of differential equation method in the design of single freeform surface optical system. Basic concepts of differential geometry are presented for understanding the derivation of partial differential equations. A numerical solution procedure is also presented. The initial condition is chosen as an additional freedom to control the image surface. Based on this approach, anastigmatic designs can be readily obtained and is used as starting point for a single reflective surface HMD design example. After optimization, the evaluation shows better MTF. Chapter 5 describes the differential equation method extended to double aspheric surface designs. For single optical surface designs, neither image surface nor the mapping from object to image can be prescribed. With one more surface added, the image surface can be prescribed. This leads to a set of three implicit ordinary differential equations. Numerical solution can be obtained by MATLAB and its procedure is also explained. An anastigmatic lens is derived from this design method and compared with an aplanatic lens. The anastigmatic design converges much faster in optimization and the final solution shows better performance.

Chloroplast protein and centrosomal genes, a tRNA intron, and odd telomeres in an unusually compact eukaryotic genome, the cryptomonad nucleomorph

Cells of several major algal groups are evolutionary chimeras of two radically different eukaryotic cells. Most of these “cells within cells” lost the nucleus of the former algal endosymbiont. But after hundreds of millions of years cryptomonads still retain the nucleus of their former red algal endosymbiont as a tiny relict organelle, the nucleomorph, which has three minute linear chromosomes, but their function and the nature of their ends have been unclear. We report extensive cryptomonad nucleomorph sequences (68.5 kb), from one end of each of the three chromosomes of Guillardia theta. Telomeres of the nucleomorph chromosomes differ dramatically from those of other eukaryotes, being repeats of the 23-mer sequence (AG)7AAG6A, not a typical hexamer (commonly TTAGGG). The subterminal regions comprising the rRNA cistrons and one protein-coding gene are exactly repeated at all three chromosome ends. Gene density (one per 0.8 kb) is the highest for any cellular genome. None of the 38 protein-coding genes has spliceosomal introns, in marked contrast to the chlorarachniophyte nucleomorph. Most identified nucleomorph genes are for gene expression or protein degradation; histone, tubulin, and putatively centrosomal ranbpm genes are probably important for chromosome segregation. No genes for primary or secondary metabolism have been found. Two of the three tRNA genes have introns, one in a hitherto undescribed location. Intergenic regions are exceptionally short; three genes transcribed by two different RNA polymerases overlap their neighbors. The reported sequences encode two essential chloroplast proteins, FtsZ and rubredoxin, thus explaining why cryptomonad nucleomorphs persist.

Compact stellarators with modular coils

Compact stellarator designs with modular coils and only two or three field periods are now available; these designs have both good stability and quasiaxial symmetry providing adequate transport for a magnetic fusion reactor. If the bootstrap current assumes theoretically predicted values a three field period configuration is optimal, but if that net current turns out to be lower, a device with two periods and just 12 modular coils might be better. There are also attractive designs with quasihelical symmetry and four or five periods whose properties depend less on the bootstrap current. Good performance requires that there be a satisfactory magnetic well in the vacuum field, which is a property lacking in a stellarator-tokamak hybrid that has been proposed for a proof of principle experiment. In this paper, we present an analysis of stability for these configurations that is based on a mountain pass theorem asserting that, if two solutions of the problem of magnetohydrodynamic equilibrium can be found, then there has to be an unstable solution. We compare results of our theory of equilibrium, stability, and transport with recently announced measurements from the large LHD experiment in Japan.

Very-long-baseline radio interferometry surveys of the compact structure in active galactic nuclei.

Very-long-baseline radio interferometry (VLBI) imaging surveys have been undertaken since the late 1970s. The sample sizes were initially limited to a few tens of objects but the snapshot technique has now allowed samples containing almost 200 sources to be studied. The overwhelming majority of powerful compact sources are asymmetric corejects of one form or another, most of which exhibit apparent superluminal motion. However 5-10% of powerful flat-spectrum sources are 100-parsec (pc)-scale compact symmetric objects; these appear to form a continuum with the 1-kpc-scale double-lobed compact steep-spectrum sources, which make up 15-20% of lower frequency samples. It is likely that these sub-galactic-size symmetric sources are the precursors to the large-scale classical double sources. There is a surprising peak around 90 degrees in the histogram of misalignments between the dominant source axes on parsec and kiloparsec scales; this seems to be associated with sources exhibiting a high degree of relativistic beaming. VLBI snapshot surveys have great cosmological potential via measurements of both proper motion and angular size vs. redshift as well as searches for gravitational "millilensing."

Morphology of high-luminosity compact radio sources.

High-dynamic range imaging and monitoring with very-long-baseline interferometry reveal a rich morphology of luminous flat-spectrum radio sources. One-sided core-jet structures abound, and superluminal motion is frequently measured. In a few cases, both distinct moving features and diffuse underlying jet emission can be detected. Superluminal motion seen in such sources is typically complex, on curved trajectories or ridge lines, and with variable component velocities, including stationary features. The curved trajectories seen can be modeled by helical motion within the underlying jet flow. The very-long-baseline interferometry properties of the superluminal features in the jet of 3C 345 and other similar sources can be explained by models invoking the emission from shocks, at least within the vicinity of the compact core. Inverse-Compton calculations, constrained by x-ray observations, yield realistic estimates for the physical conditions in the parsec-scale jet. There is evidence for a transition region in this source beyond which other factors (e.g., plasma interactions and nonsynchrotron radiation processes) may become prominent. Multifrequency and polarization imaging (especially at high frequencies) are emerging as critical tools in testing model predictions.

Structure and evolution of the compact radio source in NGC 1275.

Investigations of the fine-scale structure in the compact nucleus of the radio source 3C 84 in NGC 1275 (New General Catalogue number) are reported. Structural monitoring observations beginning as early as 1976, and continuing to the present, revealed subluminal motions in a jet-like relatively diffuse region extending away from a flat-spectrum core. A counterjet feature was discovered in 1993, and very recent nearly simultaneous studies have detected the same feature at five frequencies ranging from 5 to 43 GHz. The counterjet exhibits a strong low-frequency cutoff, giving this region of the source an inverted spectrum. The observations are consistent with a physical model in which the cutoff arises from free-free absorption in a volume that surrounds the core but obscures only the counterjet feature. If such a model is confirmed, very-long-baseline radio interferometry observations can then be used to probe the accretion region, outside the radio jet, on parsec scales.

Bidirectional motion observed in the compact symmetric object 1946+708.

We present the first direct measurements of bidirectional motions in an extragalactic radio jet. The radio source 1946+708 is a compact symmetric object with striking S-symmetry identified with a galaxy at a redshift of 0.101. From observations 2 years apart we have determined the velocities of four compact components in the jet, the fastest of which has an apparent velocity of 1.09 h-1c. By pairing up the components, assuming they were simultaneously ejected in opposite directions, we derive a 1 lower limit on the Hubble constant, H0 > 42 km.s-1.Mpc-1.

Compact steep-spectrum sources and the unified scheme.

The compact steep-spectrum sources (CSSs) are an interesting class of objects which are of subgalactic dimensions; they occur more frequently in high-frequency surveys because their spectra often turn over at lower frequencies. We have estimated the symmetry parameters of a well-defined sample of CSSs and compared these with the larger 3CR sources of similar luminosity to understand the evolution and the consistency of CSSs with the unified scheme. We suggest that the majority of CSSs are likely to be young sources advancing outward through an asymmetric, inhomogeneous environment to form the larger ones. The radio properties of the CSSs are consistent with the unified scheme, where the axes of the quasars are seen closer to the line of sight while the radio galaxies lie closer to the plane of the sky. We discuss how radio polarization observations may be used to probe whether the physical conditions in the central regions of the CSSs are different from the larger ones. We present a simple scenario where the depolarization and high rotation measures seen in many CSSs can be consistent with the low rotation measures of cores in the more extended quasars and suggest further observations to test this scenario.

Three-dimensional inverse modelling of magnetic anomaly sources based on a genetic algorithm.

We present a modelling method to estimate the 3-D geometry and location of homogeneously magnetized sources from magnetic anomaly data. As input information, the procedure needs the parameters defining the magnetization vector (intensity, inclination and declination) and the Earth's magnetic field direction. When these two vectors are expected to be different in direction, we propose to estimate the magnetization direction from the magnetic map. Then, using this information, we apply an inversion approach based on a genetic algorithm which finds the geometry of the sources by seeking the optimum solution from an initial population of models in successive iterations through an evolutionary process. The evolution consists of three genetic operators (selection, crossover and mutation), which act on each generation, and a smoothing operator, which looks for the best fit to the observed data and a solution consisting of plausible compact sources. The method allows the use of non-gridded, non-planar and inaccurate anomaly data and non-regular subsurface partitions. In addition, neither constraints for the depth to the top of the sources nor an initial model are necessary, although previous models can be incorporated into the process. We show the results of a test using two complex synthetic anomalies to demonstrate the efficiency of our inversion method. The application to real data is illustrated with aeromagnetic data of the volcanic island of Gran Canaria (Canary Islands).

Caught in the act: gas and stellar velocity dispersions in a fast Quenching compact star-forming galaxy at z ~ 1.7

We present Keck I MOSFIRE spectroscopy in the Y and H bands of GDN-8231, a massive, compact, star-forming galaxy at a redshift of z ~ 1.7. Its spectrum reveals both Hα and [Nii] emission lines and strong Balmer absorption lines. The Hα and Spitzer MIPS 24 μm fluxes are both weak, thus indicating a low star-formation rate of SFR≲5-10 M_⨀ yr−1. This, added to a relatively young age of ~700 Myr measured from the absorption lines, provides the first direct evidence for a distant galaxy being caught in the act of rapidly shutting down its star formation. Such quenching allows GDN-8231 to become a compact, quiescent galaxy, similar to three other galaxies in our sample, by z ~ 1.5. Moreover, the color profile of GDN-8231 shows a bluer center, consistent with the predictions of recent simulations for an early phase of inside-out quenching. Its line-of-sight velocity dispersion for the gas, σ_LOG^gas = 127 ± 32 km s^−1, is nearly 40% smaller than that of its stars, σ_LOG^* = 215 ± 35 km s^−1. High-resolution hydro-simulations of galaxies explain such apparently colder gas kinematics of up to a factor of ~1.5 with rotating disks being viewed at different inclinations and/or centrally concentrated star-forming regions. A clear prediction is that their compact, quiescent descendants preserve some remnant rotation from their star-forming progenitors.