Architecture brings together diverse elements to enhance the observer’s measure of esthetics and the convenience of
functionality. Architects often conceptualize synthesis of design elements to invoke the observer’s sense of harmony and
positive affect. How does an observer’s brain respond to harmony of design in interior spaces? One implicit
consideration by architects is the role of guided visual attention by observers while navigating indoors. Prior visual
experience of natural scenes provides the perceptual basis for Gestalt of design elements. In contrast, Gestalt of
organization in design varies according to the architect’s decision. We outline a quantitative theory to measure the
success in utilizing the observer’s psychological factors to achieve the desired positive affect. We outline a unified
framework for perception of geometry and motion in interior spaces, which integrates affective and cognitive aspects of
human vision in the context of anthropocentric interior design. The affective criteria are derived from contemporary
theories of interior design. Our contribution is to demonstrate that the neural computations in an observer’s eye
movement could be used to elucidate harmony in perception of form, space and motion, thus a measure of goodness of
interior design. Through mathematical modeling, we argue the plausibility of the relevant hypotheses.
KEYWORDS: Video, Computer programming, Dynamical systems, Principal component analysis, Video processing, Feature extraction, Video surveillance, Data processing, Image segmentation, Video coding
An interesting problem in analysis of video data concerns design of algorithms that detect perceptually significant features in an unsupervised manner, for instance methods of machine learning for automatic classification of human expression. A geometric formulation of this genre of problems could be modeled with help of perceptual psychology. In this article, we outline one approach for a special case where video segments are to be classified according to expression of emotion or other similar facial motions. The encoding of realistic facial motions that convey expression of emotions for a particular person P forms a parameter space XP whose study reveals the “objective geometry” for the problem of unsupervised feature detection from video. The geometric features and discrete representation of the space XP are independent of subjective evaluations by observers. While the “subjective geometry” of XP varies from observer to observer, levels of sensitivity and variation in perception of facial expressions appear to share a certain level of universality among members of similar cultures. Therefore, statistical geometry of invariants of XP for a sample of population could provide effective algorithms for extraction of such features. In cases where frequency of events is sufficiently large in the sample data, a suitable framework could be provided to facilitate the information-theoretic organization and study of statistical invariants of such features. This article provides a general approach to encode motion in terms of a particular genre of dynamical systems and the geometry of their flow. An example is provided to illustrate the general theory.
The ability to recognize facial expression in humans is performed with the amygdala which uses parallel processing streams to identify the expressions quickly and accurately. Additionally, it is possible that a feedback mechanism may play a role in this process as well. Implementing a model with similar parallel structure and feedback mechanisms could be used to improve current facial recognition algorithms for which varied expressions are a source for error. An anatomically constrained artificial neural-network model was created that uses this parallel processing architecture and feedback to categorize facial expressions. The presence of a feedback mechanism was not found to significantly improve performance for models with parallel architecture. However the use of parallel processing streams significantly improved accuracy over a similar network that did not have parallel architecture. Further investigation is necessary to determine the benefits of using parallel streams and feedback mechanisms in more advanced object recognition tasks.
Imaging text documents always adds a certain amount of noise and other artifacts. Fidelity of electronic reproduction depends very much on the accuracy of noise removal algorithms. The present algorithms attempt to remove artifact by filters that are based on convolution or other methods that are “invasive” with respect to the original representation of the text document. As a result, it is highly desirable to design noise removal algorithms that restore the image to the original representation of text, removing merely noise and added artifacts without blurring or tampering with font corners and edges. In this paper, we present a solution to this problem by design of a filter based on accurate statistics of text in its Matrix Frequency Representation that was developed earlier by the authors
The advent of the internet has opened a host of new and exciting questions in the science and mathematics of information organization and data mining. In particular, a highly ambitious promise of the internet is to bring the bulk of human knowledge to everyone with access to a computer network, providing a democratic medium for sharing and communicating knowledge regardless of the language of the communication. The development of sharing and communication of knowledge via transfer of digital files is the first crucial achievement in this direction. Nonetheless, available solutions to numerous ancillary problems remain far from satisfactory. Among such outstanding problems are the first few fundamental questions that have been responsible for the emergence and rapid growth of the new field of Knowledge Engineering, namely, classification of forms of data, their effective organization, and extraction of knowledge from massive distributed data sets, and the design of fast effective search engines. The precision of machine learning algorithms in classification and recognition of image data (e.g. those scanned from books and other printed documents) are still far from human performance and speed in similar tasks. Discriminating the many forms of ASCII data from each other is not as difficult in view of the emerging universal standards for file-format. Nonetheless, most of the past and relatively recent human knowledge is yet to be transformed and saved in such machine readable formats. In particular, an outstanding problem in knowledge engineering is the problem of organization and management--with precision comparable to human performance--of knowledge in the form of images of documents that broadly belong to either text, image or a blend of both. It was shown in that the effectiveness of OCR was intertwined with the success of language and font recognition.
KEYWORDS: Neural networks, Data modeling, Principal component analysis, Chemical analysis, Visualization, Information technology, Data analysis, Data acquisition, Pattern recognition, Mathematical modeling
Artificial neural network models are typically useful in pattern recognition and extraction of important features in large data sets. These models are implemented in a wide variety of contexts and with diverse type of input-output data. The underlying mathematics of supervised training of neural networks is ultimately tied to the ability to approximate the nonlinearities that are inherent in network’s generalization ability. The quality and availability of sufficient data points for training and validation play a key role in the generalization ability of the network. A potential domain of applications of neural networks is in analysis of subjective data, such as in consumer science, affective neuroscience and perception of chemical senses. In applications of ANN to subjective data, it is common to rely on knowledge of the science and context for data acquisition, for instance as a priori probabilities in the Bayesian framework. In this paper, we discuss the circumstances that create challenges for success of neural network models for subjective data analysis, such as sparseness of data and cost of acquisition of additional samples. In particular, in the case of affect and perception of chemical senses, we suggest that inherent ambiguity of subjective responses could be offset by a combination of human-machine expert. We propose a method of pre- and post-processing for blind analysis of data that that relies on heuristics from human performance in interpretation of data. In particular, we offer an information-theoretic smoothing (ITS) algorithm that optimizes that geometric visualization of multi-dimensional data and improves human interpretation of the input-output view of neural network implementations. The pre- and post-processing algorithms and ITS are unsupervised. Finally, we discuss the details of an example of blind data analysis from actual taste-smell subjective data, and demonstrate the usefulness of PCA in reduction of dimensionality, as well as ITS.
The purpose of this paper is two-fold: (a) to demonstrate that pattern recognition methods in image processing leads to a noticeable improvement in bioinformatics, specifically, analysis of microarray data in gene expression correlated to cancer; (b) to bring the utility of geometric methods in pattern recognition to attention of researchers in bioinformatics and molecular biologists. Our method of analysis is seen to readily provide great improvement over the latest published methods in bioinformatics. We also hope that in the process, we provide mathematical insight into the problems of microarray data analysis from the point of view of signal processing and learning theory.
Perceptual geometry is an emerging field of interdisciplinary research whose objectives focus on study of geometry from the perspective of visual perception, and in turn, apply such geometric findings to the ecological study of vision. Perceptual geometry attempts to answer fundamental questions in perception of form and representation of space through synthesis of cognitive and biological theories of visual perception with geometric theories of the physical world. Perception of form and space are among fundamental problems in vision science. In recent cognitive and computational models of human perception, natural scenes are used systematically as preferred visual stimuli. Among key problems in perception of form and space, we have examined perception of geometry of natural surfaces and curves, e.g. as in the observer's environment. Besides a systematic mathematical foundation for a remarkably general framework, the advantages of the Gestalt theory of natural surfaces include a concrete computational approach to simulate or recreate images whose geometric invariants and quantities might be perceived and estimated by an observer. The latter is at the very foundation of understanding the nature of perception of space and form, and the (computer graphics) problem of rendering scenes to visually invoke virtual presence.
The aims of this series of papers are: (a) to formulate a geometric framework for non-linear analysis of global features of massive data sets; and (b) to quantify non-linear dependencies among (possibly) uncorrelated parameters that describe the data. In this paper, we consider an application of the methods to extract and characterize nonlinearities in the functional magnetic resonance imaging data and EEG of human brain (fMRI). A more general treatment of this theory applies to a wider variety of massive data sets; however, the usual technicalities for computation and accurate interpretation of abstract concepts remain a challenge for each individual area of application.
Principal and Independent Component Analysis (PCA and ICA) are popular and powerful methods for approximation, regression, blind source separation and numerous other statistical tasks. These methods have inherent linearity assumptions that limit their applicability to globally estimate massive and realistic data sets in terms of a few parameters. Global description of such data sets requires more versatile nonlinear methods. Nonetheless, modification of PCA and ICA can be used in a variety of circumstances to discover the underlying non-linear features of the data set. Differential topology and Riemannian geometry have developed systematic methods for local-to-global integration of linearizable features. Numerical methods from approximation theory are applicable to provide a discrete and algorithmic adaptation of continuous topological methods. Such nonlinear descriptions have a far smaller number of parameters than the dimension of the feature space. In addition, it is possible to describe nonlinear relationship between such parameters. We present the mathematical framework for the extension of these methods to a robust estimate for non-linear PCA. We discuss the application of this technique to the study of the topology of the space of parameters in human image databases.
Efficient and robust representation of signals has been the focus of a number of areas of research. Wavelets represent one such representation scheme that enjoys desirable qualitites such as time-frequency localization. Once the Mother wavelet has been selected, other wavelets can be generated as translated and dilated versions of the Mother wavelet in the 1D case. In the 2D case tensor product of two 1D wavelets is the most often used transform. Over complete representation of wavelets has proved to be of great advantage, both in sparse coding of complex scenes and multi-media data compression. On the other hand over completeness raises a number of technical difficulties for robust computation and systematic generalization of constructions beyond their original application domains.
In biological and computational vision, the perception and description of geometric attributes of surfaces in natural scenes has received a great deal of attention. The physical and geometric properties of surfaces related to their optical characteristics depend on their texture. In previous work, we introduced the concept of the Gestalt of a surface. The Gestalt being a geometric object that retains the mathematical properties of the surface. The Gestalt is determined using the theory of Riemannian foliations from differential topology and the concept of an observer's subjective function in a probabilistic manner. In this paper, we continue our study of geometry of natural surfaces with textures that exhibit statistical regularity at some resolution. It appears that all earlier algorithms in computer vision for extraction of shape attributes from texture have made some (piecewise) smoothness assumption about the surfaces under study. However, natural surfaces, as well as most synthetic ones are not smooth in the mathematical sense. Hence, the domain of applicability of current algorithms is severely limited. We propose algorithms to estimate geometric invariants of textured surfaces that are not necessarily smooth, but possess a statistically regular structure. An important step is based on a learning theoretic method for parameterization of textured surfaces. This method takes into account the statistical texture information in a 2D image of the surface. From a dictionary of geometry for the parameter space, a supervised artificial neural network selects the optimal choice for parameterization. As a result, the algorithms for shape from texture (slant, tilt, curvature...) have a more efficient implementation and a faster runtime. In this paper, we explain the significance of statistically symmetric patterns on surfaces. We show how such texture regularity can be used to solve the linearized problem, leaving the full details of the linearization of the Gestalt of surfaces to a forthcoming paper. The solution of the linearized problem together with algorithms to linearized surface Gestalts provide the desired estimates for the geometric features of natural surfaces with statistically regular textures at some scale.
KEYWORDS: Visualization, Visual process modeling, Intelligence systems, Principal component analysis, Eye, Data processing, Natural surfaces, Brain, Retina, Visual system
In Vision Geometry '99 we introduced the Gestalt approach to perceptual approximation of surfaces in natural scenes; that is, as a geometric theory retaining certain mathematical properties of surfaces while adhering to the human perceptual organization of vision. The theory of curves follows the same philosophy, relying on optical properties of physical objects whose features in the scale and resolution -- imposed by the observer -- afford 'a one-dimensional Gestalt.' The Gestalt theory of curves and surfaces is part of the Perceptual Geometry of the natural world that hypothetically evolves within intelligent systems capable of retaining partial information from stimuli in 'memory' and visual 'learning' through 'brain plasticity.' Perceptual geometry aims at explaining geometry from the perspective of visual perception, and in turn, how to apply such geometric findings to the ecological study of vision. Perceptual geometry attempts to answer fundamental questions in perception of form and representation of space through synthesis of cognitive and biological theories of visual perception with geometric theories of the physical world. Algorithms in this theory are typically presented based on a combination of a mathematical formulation of eye-movements and multi-scale multi-resolution filtering. In this paper, methods from statistical pattern recognition are applied to explain the learning-theoretic and perceptual analogs of geometric theory of space and its objects optically defined by curves and surfaces. The human visual system recovers depth from the visual stimuli registered on the two-dimensional surface of the retina by means of a variety of mechanisms, from bottom-up (such as stereopsis and motion parallax) to top-down influences. Perception and representation of space and objects within the visual environment rely on combination of a multitude of such mechanisms. The problem of modeling cortical representation of visual information is, therefore, very complex and challenging.
Neural Networks and Neurocomputing provide a natural paradigm for parallel and distributed processing. Neurocomputing within the context of classical computation have been used for approximation and classification tasks with some success. In this paper we propose a model for Quantum Neurocomputation and explore some of its properties and potential applications to pattern recognition.
It is often the case that information about a process can be obtained using a variety of methods. Each method is employed because of specific advantages over the competing alternatives. An example in medical neuro-imaging is the choice between fMRI and MEG modes where fMRI can provide high spatial resolution in comparison to the superior temporal resolution of MEG. The combination of data from varying modes provides the opportunity to infer results that may not be possible by means of any one mode alone. We discuss a Bayesian and learning theoretic framework for enhanced feature extraction that is particularly suited to multi-modal investigations of massive data sets from multiple experiments. In the following Bayesian approach, acquired knowledge (information) regarding various aspects of the process are all directly incorporated into the formulation. This information can come from a variety of sources. In our case, it represents statistical information obtained from other modes of data collection. The information is used to train a learning machine to estimate a probability distribution, which is used in turn by a second machine as a prior, in order to produce a more refined estimation of the distribution of events. The computational demand of the algorithm is handled by proposing a distributed parallel implementation on a cluster of workstations that can be scaled to address real-time needs if required. We provide a simulation of these methods on a set of synthetically generated MEG and EEG data. We show how spatial and temporal resolutions improve by using prior distributions. The method on fMRI signals permits one to construct the probability distribution of the non-linear hemodynamics of the human brain (real data). These computational results are in agreement with biologically based measurements of other labs, as reported to us by researchers from UK. We also provide preliminary analysis involving multi-electrode cortical recording that accompanies behavioral data in pain experiments on freely moving mice subjected to moderate heat delivered by an electric bulb. Summary of new or breakthrough ideas: (1) A new method to estimate probability distribution for measurement of nonlinear hemodynamics of brain from a multi- modal neuronal data. This is the first time that such an idea is tried, to our knowledge. (2) Breakthrough in improvement of time resolution of fMRI signals using (1) above.
KEYWORDS: Independent component analysis, Intelligence systems, Principal component analysis, 3D modeling, Motion models, Mathematical modeling, Visual process modeling, Visualization, Statistical analysis, Signal to noise ratio
In standard differential geometry, the Fundamental Theorem of Space Curves states that two differential invariants of a curve, namely curvature and torsion, determine its geometry, or equivalently, the isometry class of the curve up to rigid motions in the Euclidean three-dimensional space. Consider a physical model of a space curve made from a sufficiently thin, yet visible rigid wire, and the problem of perceptual identification (by a human observer or a robot) of two given physical model curves. In a previous paper (perceptual geometry) we have emphasized a learning theoretic approach to construct a perceptual geometry of the surfaces in the environment. In particular, we have described a computational method for mathematical representation of objects in the perceptual geometry inspired by the ecological theory of Gibson, and adhering to the principles of Gestalt in perceptual organization of vision. In this paper, we continue our learning theoretic treatment of perceptual geometry of objects, focusing on the case of physical models of space curves. In particular, we address the question of perceptually distinguishing two possibly novel space curves based on observer's prior visual experience of physical models of curves in the environment. The Fundamental Theorem of Space Curves inspires an analogous result in perceptual geometry as follows. We apply learning theory to the statistics of a sufficiently rich collection of physical models of curves, to derive two statistically independent local functions, that we call by analogy, the curvature and torsion. This pair of invariants distinguish physical models of curves in the sense of perceptual geometry. That is, in an appropriate resolution, an observer can distinguish two perceptually identical physical models in different locations. If these pairs of functions are approximately the same for two given space curves, then after possibly some changes of viewing planes, the observer confirms the two are the same.
In this paper, we propose a new measure of novelty detection for target selection in visual scenes. Our approach to the definition of novelty is based on the use of local kernels and Fisher information metric in the context of support vector machine regression. We discuss the applications in the specific context of visual saccades as a mechanism of search and discuss naturel generations of the approach in other contexts. We also propose natural regularization approaches arising from consideration of the problem that can be applied to learning machines including the SVM.
The concept of space and geometry varies across the subjects. Following Poincare, we consider the construction of the perceptual space as a continuum equipped with a notion of magnitude. The study of the relationships of objects in the perceptual space gives rise to what we may call perceptual geometry. Computational modeling of objects and investigation of their deeper perceptual geometrical properties (beyond qualitative arguments) require a mathematical representation of the perceptual space. Within the realm of such a mathematical/computational representation, visual perception can be studied as in the well-understood logic-based geometry. This, however, does not mean that one could reduce all problems of visual perception to their geometric counterparts. Rather, visual perception as reported by a human observer, has a subjective factor that could be analytically quantified only through statistical reasoning and in the course of repetitive experiments. Thus, the desire to experimentally verify the statements in perceptual geometry leads to an additional probabilistic structure imposed on the perceptual space, whose amplitudes are measured through intervention by human observers. We propose a model for the perceptual space and the case of perception of textured surfaces as a starting point for object recognition. To rigorously present these ideas and propose computational simulations for testing the theory, we present the model of the perceptual geometry of surfaces through an amplification of theory of Riemannian foliation in differential topology, augmented by statistical learning theory. When we refer to the perceptual geometry of a human observer, the theory takes into account the Bayesian formulation of the prior state of the knowledge of the observer and Hebbian learning. We use a Parallel Distributed Connectionist paradigm for computational modeling and experimental verification of our theory.
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