A Viking Lander 1 image was modeled as mixtures of reflectance spectra of palagonite dust, gray andesitelike rock, and a coarse rocklike soil. The rocks are covered to varying degrees by dust but otherwise appear unweathered. Rocklike soil occurs as lag deposits in deflation zones around stones and on top of a drift and as a layer in a trench dug by the lander. This soil probably is derived from the rocks by wind abrasion and/or spallation. Dust is the major component of the soil and covers most of the surface. The dust is unrelated spectrally to the rock but is equivalent to the global-scale dust observed telescopically. A new method was developed to model a multispectral image as mixtures of end-member spectra and to compare image spectra directly with laboratory reference spectra. The method for the first time uses shade and secondary illumination effects as spectral end-members; thus the effects of topography and illumination on all scales can be isolated or removed. The image was calibrated absolutely from the laboratory spectra, in close agreement with direct calibrations. The method has broad applications to interpreting multispectral images, including satellite images.

Spectral mixture modeling - A new analysis of rock and soil types at the Viking Lander 1 site. [on Mars]

Derivatives, mostly in the form of gradients and Hessians, are ubiquitous in machine learning. Automatic differentiation (AD), also called algorithmic differentiation or simply "auto-diff", is a family of techniques similar to but more general than backpropagation for efficiently and accurately evaluating derivatives of numeric functions expressed as computer programs. AD is a small but established field with applications in areas including computational uid dynamics, atmospheric sciences, and engineering design optimization. Until very recently, the fields of machine learning and AD have largely been unaware of each other and, in some cases, have independently discovered each other's results. Despite its relevance, general-purpose AD has been missing from the machine learning toolbox, a situation slowly changing with its ongoing adoption under the names "dynamic computational graphs" and "differentiable programming". We survey the intersection of AD and machine learning, cover applications where AD has direct relevance, and address the main implementation techniques. By precisely defining the main differentiation techniques and their interrelationships, we aim to bring clarity to the usage of the terms "autodiff", "automatic differentiation", and "symbolic differentiation" as these are encountered more and more in machine learning settings.

/pdf/automatic-differentiation-in-machine-learning-a-survey-4s77ht2sqh.pdf

Automatic differentiation in machine learning: a survey

This paper describes a benchmark for evaluation of 3D mesh segmentation salgorithms. The benchmark comprises a data set with 4,300 manually generated segmentations for 380 surface meshes of 19 different object categories, and it includes software for analyzing 11 geometric properties of segmentations and producing 4 quantitative metrics for comparison of segmentations. The paper investigates the design decisions made in building the benchmark, analyzes properties of human-generated and computer-generated segmentations, and provides quantitative comparisons of 7 recently published mesh segmentation algorithms. Our results suggest that people are remarkably consistent in the way that they segment most 3D surface meshes, that no one automatic segmentation algorithm is better than the others for all types of objects, and that algorithms based on non-local shape features seem to produce segmentations that most closely resemble ones made by humans.

https://www.cs.princeton.edu/~funk/segeval.pdf

A benchmark for 3D mesh segmentation

Recent advances in airborne and spaceborne hyperspectral imaging technology have provided end users with rich spectral, spatial, and temporal information. They have made a plethora of applications feasible for the analysis of large areas of the Earth?s surface. However, a significant number of factors-such as the high dimensions and size of the hyperspectral data, the lack of training samples, mixed pixels, light-scattering mechanisms in the acquisition process, and different atmospheric and geometric distortions-make such data inherently nonlinear and complex, which poses major challenges for existing methodologies to effectively process and analyze the data sets. Hence, rigorous and innovative methodologies are required for hyperspectral image (HSI) and signal processing and have become a center of attention for researchers worldwide.

/pdf/advances-in-hyperspectral-image-and-signal-processing-a-4kxt4zjyeh.pdf

Advances in Hyperspectral Image and Signal Processing: A Comprehensive Overview of the State of the Art

Volumetric grid is widely used for 3D deep learning due to its regularity. However the use of relatively lower order local approximation functions such as piece-wise constant function (occupancy grid) or piece-wise linear function (distance field) to approximate 3D shape means that it needs a very high-resolution grid to represent finer geometry details, which could be memory and computationally inefficient. In this work, we propose the PointGrid, a 3D convolutional network that incorporates a constant number of points within each grid cell thus allowing the network to learn higher order local approximation functions that could better represent the local geometry shape details. With experiments on popular shape recognition benchmarks, PointGrid demonstrates state-of-the-art performance over existing deep learning methods on both classification and segmentation.

/pdf/pointgrid-a-deep-network-for-3d-shape-understanding-1a5lreyclw.pdf

PointGrid: A Deep Network for 3D Shape Understanding

A detailed discussion of the point in polygon problem for arbitrary polygons is given. Two concepts for solving this problem are known in literature: the even–odd ruleand the winding number, the former leading to ray-crossing, the latter to angle summationalgorithms. First we show by mathematical means that both concepts are very closely related, thereby developing a first version of an algorithm for determining the winding number. Then we examine how to accelerate this algorithm and how to handle special cases. Furthermore we compare these algorithms with those found in literature and discuss the results.  2001 Elsevier Science B.V. All rights reserved.

/pdf/the-point-in-polygon-problem-for-arbitrary-polygons-1d5nu79y4o.pdf

The point in polygon problem for arbitrary polygons

Linear spectral unmixing aims at estimating the number of pure spectral substances, also called endmembers , their spectral signatures, and their abundance fractions in remotely sensed hyperspectral images. This paper describes a method for unsupervised hyperspectral unmixing called minimum volume simplex analysis (MVSA) and introduces a new computationally efficient implementation. MVSA approaches hyperspectral unmixing by fitting a minimum volume simplex to the hyperspectral data, constraining the abundance fractions to belong to the probability simplex. The resulting optimization problem, which is computationally complex, is solved in this paper by implementing a sequence of quadratically constrained subproblems using the interior point method, which is particularly effective from the computational viewpoint. The proposed implementation (available online: www.lx.it.pt/%7ejun/DemoMVSA.zip) is shown to exhibit state-of-the-art performance not only in terms of unmixing accuracy, particularly in nonpure pixel scenarios, but also in terms of computational performance. Our experiments have been conducted using both synthetic and real data sets. An important assumption of MVSA is that pure pixels may not be present in the hyperspectral data, thus addressing a common situation in real scenarios which are often dominated by highly mixed pixels. In our experiments, we observe that MVSA yields competitive performance when compared with other available algorithms that work under the nonpure pixel regime. Our results also demonstrate that MVSA is well suited to problems involving a high number of endmembers (i.e., complex scenes) and also for problems involving a high number of pixels (i.e., large scenes).

/pdf/minimum-volume-simplex-analysis-a-fast-algorithm-for-linear-w2zklt6y4w.pdf

Minimum Volume Simplex Analysis: A Fast Algorithm for Linear Hyperspectral Unmixing

D mesh segmentation is a fundamental process for Digital Shape Reconstruction in a variety of applications including Reverse Engineering, Medical Imaging, etc. It is used to provide a high level representation of the raw 3D data which is required for CAD, CAM and CAE. In this paper, we present an exhaustive overview of 3D mesh segmentation methodologies examining their suitability for CAD models. In particular, a classification of the various methods is given based on their corresponding underlying fundamental methodology concept as well as on the distinct criteria and features used in the segmentation process.

/pdf/3d-mesh-segmentation-methodologies-for-cad-applications-cjycop0kfn.pdf

3D Mesh Segmentation Methodologies for CAD applications

Modeling 3D objects from sketches is a process that requires several challenging problems including segmentation, recognition and reconstruction. Some of these tasks are harder for humans and some are harder for the machine. At the core of the problem lies the need for semantic understanding of the shape’s geometry from the sketch. In this paper we propose a method to model 3D objects from sketches by utilizing humans specifically for semantic tasks that are very simple for humans and extremely difficult for the machine, while utilizing the machine for tasks that are harder for humans. The user assists recognition and segmentation by choosing and placing specific geometric primitives on the relevant parts of the sketch. The machine first snaps the primitive to the sketch by fitting its projection to the sketch lines, and then improves the model globally by inferring geosemantic constraints that link the different parts. The fitting occurs in real-time, allowing the user to be only as precise as needed to have a good starting configuration for this non-convex optimization problem. We evaluate the accessibility of our approach with a user study.

/pdf/geosemantic-snapping-for-sketch-based-modeling-23l3qu4rxr.pdf

Geosemantic Snapping for Sketch-Based Modeling

Most blind hyperspectral unmixing methods exploit convex geometry properties of hyperspectral data. The minimum volume simplex analysis (MVSA) is one of such methods, which, as many others, estimates the minimum volume (MV) simplex where the measured vectors live. MVSA was conceived to circumvent the matrix factorization step often implemented by MV-based algorithms and also to cope with outliers, which compromise the results produced by MV algorithms. Inspired by the recently proposed robust MV enclosing simplex (RMVES) algorithm, we herein introduce the robust MVSA (RMVSA), which is a version of MVSA robust to noise. As in RMVES, the robustness is achieved by employing chance constraints, which control the volume of the resulting simplex. RMVSA differs, however, substantially from RMVES in the way optimization is carried out. In this paper, we develop a linearization relaxation of the nonlinear chance constraints, which can greatly lighten the computational complex of chance constraint problems. The effectiveness of RMVSA is illustrated by comparing its performance with the state of the art.

https://www.umbc.edu/rssipl/people/aplaza/Papers/Conferences/2014.EUSIPCO.RMVSA.pdf

Alexander Agathos

Papers

The point in polygon problem for arbitrary polygons

Minimum Volume Simplex Analysis: A Fast Algorithm for Linear Hyperspectral Unmixing

3D Mesh Segmentation Methodologies for CAD applications

Geosemantic Snapping for Sketch-Based Modeling

Robust Minimum Volume Simplex Analysis for Hyperspectral Unmixing