Biomedical Image Analysis: Rapid prototyping with Mathematica

Digital acquisition techniques have caused an explosion in the production of medical images, especially with the advent of multi-slice CT and volume MRI. One third of the financial investments in a modern hospital's equipment are dedicated to imaging. Emerging screening programs add to this flood of data. The capabilities of many recent computer-aided diagnosis (CAD) programs are compelling, and have recently lead to many new CAD companies. This calls for many new algorithms for image analysis and dedicated scientists for the job.Image analysis software libraries abound, but unfortunately are often limited in functionality, are too specific, or need a rather dedicated environment and have a long learning curve. Today's computer vision algorithms are based on solid mathematics, requiring a highly versatile, high level mathematical prototyping environment. We have chosen Mathematica by Wolfram Research Inc., and describe the successful results of the first 2.5 years of its use in the training of biomedical engineers in image analysis

Effects of Ground Manifold Modeling on the Accuracy of Stixel Calculations

This paper highlights the role of ground manifold modeling for stixel calculations; stixels are medium-level data representations used for the development of computer vision modules for self-driving cars. By using single-disparity maps and simplifying ground manifold models, calculated stixels may suffer from noise, inconsistency, and false-detection rates for obstacles, especially in challenging datasets. Stixel calculations can be improved with respect to accuracy and robustness by using more adaptive ground manifold approximations. A comparative study of stixel results, obtained for different ground-manifold models (e.g., plane-fitting, line-fitting in v-disparities or polynomial approximation, and graph cut), defines the main part of this paper. This paper also considers the use of trinocular stereo vision and shows that this provides options to enhance stixel results, compared with the binocular recording. Comprehensive experiments are performed on two publicly available challenging datasets. We also use a novel way for comparing calculated stixels with ground truth. We compare depth information, as given by extracted stixels, with ground-truth depth, provided by depth measurements using a highly accurate LiDAR range sensor (as available in one of the public datasets). We evaluate the accuracy of four different ground-manifold methods. The experimental results also include quantitative evaluations of the tradeoff between accuracy and run time. As a result, the proposed trinocular recording together with graph-cut estimation of ground manifolds appears to be a recommended way, also considering challenging weather and lighting conditions

Self-Ordering Point Clouds

In this paper we address the task of finding representative subsets of points in a 3D point cloud by means of a point-wise ordering. Only a few works have tried to address this challenging vision problem, all with the help of hard to obtain point and cloud labels. Different from these works, we introduce the task of point-wise ordering in 3D point clouds through self-supervision, which we call self-ordering. We further contribute the first end-to-end trainable network that learns a point-wise ordering in a self-supervised fashion. It utilizes a novel differentiable point scoring-sorting strategy and it constructs an hierarchical contrastive scheme to obtain self-supervision signals. We extensively ablate the method and show its scalability and superior performance even compared to supervised ordering methods on multiple datasets and tasks including zero-shot ordering of point clouds from unseen categories

Image hierarchy in gaussian scale space

We investigate the topological structure of an image and the hierarchical relationship between local and global structures provided by spatial gradients at different levels of scale in the Gaussian scale space. The gradient field curves link stationary points of an image, including a local minimum at infinity, and construct the topological structure of the image. The evolution of the topological structure with respect to scale is analyzed using pseudograph representation. The hierarchical relationships among the structures at different scales are expressed as trajectories of the stationary points in the scale space, which we call the stationary curves. Each top point of the local extremum curve generically has a specific gradient field curve, which we call the antidirectional figure-flow curve. The antidirectional figure-flow curve connects the top-point and another local extremum to which the toppoint is subordinate. A point at infinity can also be connected to the top points of local minimum curves. These hierarchical relationships among the stationary points are expressed as a tree. This tree expresses a hierarchical structure of dominant parts. We clarify the graphical grammar for the construction of this tree in the Gaussian scale space. Furthermore, we show a combinatorial structure of singular points in the Gaussian scale space using conformal mapping from Euclidean space to the spherical surface. We define segment edges as a zero-crossing set in the Gaussian scale space using the singular points. An image in the Gaussian scale space is the convolution of the image and the Gaussian kernel. The Gaussian kernel of an appropriate variance is a typical presmoothing operator for segmentation. The variance is heuristically selected using statistics of images such as the noise distribution in images. The variance of the kernel is determined using the singular-point configuration in the Gaussian scale space, since singular points in the Gaussian scale space allow the extraction of the dominant parts of an image. This scale-selection strategy derives the hierarchical structure of the segments. Unsupervised segmentation methods, however, have difficulty in distinguishing valid segments associated with the objects from invalid random segments due to noise. By showing that the number of invalid segments monotonically decreases with increasing scale, we characterize the valid and invalid segments in the Gaussian scale space. This property allows us to identify the valid segments from coarse to fine and does us to prevent undersegmentation and oversegmentation. Finally, we develop principal component analysis (PCA) of a point cloud on the basis of the scale-space representation of its probability density function. We explain the geometric features of a point cloud in the Gaussian scale space and observe reduced dimensionality with respect to the loss of information. Furthermore, we introduce a hierarchical clustering of the point cloud and analyze the statistical significance of the clusters and their subspaces. Moreover, we present a mathematical framework of the scale-based PCA, which derives a statistically reasonable criterion for choosing the number of components to retain or reduce the dimensionality of a point cloud. Finally, we also develop a segmentation algorithm using configurations of singular points in the Gaussian scale space

Optimising Spatial and Tonal Data for PDE-based Inpainting

Some recent methods for lossy signal and image compression store only a few selected pixels and fill in the missing structures by inpainting with a partial differential equation (PDE). Suitable operators include the Laplacian, the biharmonic operator, and edge-enhancing anisotropic diffusion (EED). The quality of such approaches depends substantially on the selection of the data that is kept. Optimising this data in the domain and codomain gives rise to challenging mathematical problems that shall be addressed in our work. In the 1D case, we prove results that provide insights into the difficulty of this problem, and we give evidence that a splitting into spatial and tonal (i.e. function value) optimisation does hardly deteriorate the results. In the 2D setting, we present generic algorithms that achieve a high reconstruction quality even if the specified data is very sparse. To optimise the spatial data, we use a probabilistic sparsification, followed by a nonlocal pixel exchange that avoids getting trapped in bad local optima. After this spatial optimisation we perform a tonal optimisation that modifies the function values in order to reduce the global reconstruction error. For homogeneous diffusion inpainting, this comes down to a least squares problem for which we prove that it has a unique solution. We demonstrate that it can be found efficiently with a gradient descent approach that is accelerated with fast explicit diffusion (FED) cycles. Our framework allows to specify the desired density of the inpainting mask a priori. Moreover, is more generic than other data optimisation approaches for the sparse inpainting problem, since it can also be extended to nonlinear inpainting operators such as EED. This is exploited to achieve reconstructions with state-of-the-art quality. We also give an extensive literature survey on PDE-based image compression methods

Efficient Crisis Management by Selection and Analysis of Relief Centers in Disaster Integrating GIS and Multicriteria Decision Methods: A Case Study of Tehran

In Iran, location is usually done by temporary relief organizations without considering the necessary standards or conditions. The inappropriate and unscientific location may have led to another catastrophe, even far greater than the initial tragedy. In this study, the proposed locations of crisis management in the region and the optimal points proposed by the Geographic Information System (GIS), taking into account the opinions of experts and without the opinion of experts, were evaluated according to 18 criteria. First, the optimal areas have been evaluated according to standard criteria extracted by GIS and the intended locations of the region for accommodation in times of crisis. Then, the position of each place is calculated concerning each criterion. The resulting matrix of optimal options was qualitatively entered into the Preference Ranking Organization Method for Evaluation (PROMETHEE) for analysis. The triangular fuzzy aggregation method for weighting and standard classification of criteria for extracting optimal areas using GIS and integrating entropy and the Multiobjective Optimization Based on Ratio Analysis (MOORA) method for prioritizing places in the region are considered in this research. Finally, by applying constraints and using net input and output flows, optimal and efficient options are identified by PROMETHEE V. Among the research options, only four options were optimal and efficient. A case study of the Tehran metropolis is provided to show the ability of the proposed approach for selecting the points in three modes, with/without applying weights and applying crisis management

Human activity recognition for the use in intelligent spaces

The aim of this Graduation Project is to develop a generic biological inspired activity recognition system for the use in intelligent spaces. Intelligent spaces form the context for this project. The goal is to develop a working prototype that can learn and recognize human activities from a limited training set in all kinds of spaces and situations. For testing purposes, the office environment is chosen as subject for the intelligent space. The purpose of the intelligent space, in this case the office, is left out of the scope of the project. The scope is limited to the perceptive system of the intelligent space. The notion is that the prototype should not be bound to a specific space, but it should be a generic perceptive system able to cope in any given space within the build environment. The fact that no space is the same, developing a prototype without any domain knowledge in which it can learn and recognize activities, is the main challenge of this project. In al layers of the prototype, the data processing is kept as abstract and low level as possible to keep it as generic as possible. This is done by using local features, scale invariant descriptors and by using hidden Markov models for pattern recognition. The novel approach of the prototype is that it combines structure as well as motion features in one system making it able to train and recognize a variety of activities in a variety of situations. From rhythmic expressive actions with a simple cyclic pattern to activities where the movement is subtle and complex like typing and reading, can all be trained and recognized. The prototype has been tested on two very different data sets. The first set in which the videos are shot in a controlled environment in which simple actions were performed. The second set in which videos are shot in a normal office where daily office activities are captured and categorized afterwards. The prototype has given some promising results proving it can cope with very different spaces, actions and activities. The aim of this Graduation Project is to develop a generic biological inspired activity recognition system for the use in intelligent spaces. Intelligent spaces form the context for this project. The goal is to develop a working prototype that can learn and recognize human activities from a limited training set in all kinds of spaces and situations. For testing purposes, the office environment is chosen as subject for the intelligent space. The purpose of the intelligent space, in this case the office, is left out of the scope of the project. The scope is limited to the perceptive system of the intelligent space. The notion is that the prototype should not be bound to a specific space, but it should be a generic perceptive system able to cope in any given space within the build environment. The fact that no space is the same, developing a prototype without any domain knowledge in which it can learn and recognize activities, is the main challenge of this project. In al layers of the prototype, the data processing is kept as abstract and low level as possible to keep it as generic as possible. This is done by using local features, scale invariant descriptors and by using hidden Markov models for pattern recognition. The novel approach of the prototype is that it combines structure as well as motion features in one system making it able to train and recognize a variety of activities in a variety of situations. From rhythmic expressive actions with a simple cyclic pattern to activities where the movement is subtle and complex like typing and reading, can all be trained and recognized. The prototype has been tested on two very different data sets. The first set in which the videos are shot in a controlled environment in which simple actions were performed. The second set in which videos are shot in a normal office where daily office activities are captured and categorized afterwards. The prototype has given some promising results proving it can cope with very different spaces, actions and activities

Developower: The Potential Motivity in Economic Process

Stating from the intrinsic characteristics of macroeconomic process, this paper puts forward the concept of developwer and its theoretical frame. The developwer is the potential and invisible motivities to push economy to progress. By means of the developower theory, we can explain some important problems in macro-economy. We discuss the basic properties of developower and obtain some interesting inferences. The evaluating approaches are given for one or more developowers, and then we can measure them in analytic way and analyze the correlated effects among them. Finally, we illustrate that the developower movements exist widely in the social and economic development