Perspex machine

We introduce the perspex machine which unifies projective geometry and the Turing machine, resulting in a supra-Turing machine. Specifically, we show that a Universal Register Machine (URM) can be implemented as a conditional series of whole numbered projective transformations. This leads naturally to a suggestion that it might be possible to construct a perspex machine as a series of pin-holes and stops. A rough calculation shows that an ultraviolet perspex machine might operate up to the petahertz range of operations per second. Surprisingly, we find that perspex space is irreversible in time, which might make it a candidate for an anisotropic spacetime geometry in physical theories. We make a bold hypothesis that the apparent irreversibility of physical time is due to the random nature of quantum events, but suggest that a sum over histories might be achieved by sampling fluctuations in the direction of time flow. We propose an experiment, based on the Casimir apparatus, that should measure fluctuations of time flow with respect to time duration- if such fluctuations exist.

Representing geometrical knowledge

This paper introduces perspex algebra which is being developed as a common representation of geometrical knowledge. A perspex can currently be interpreted in one of four ways. First, the algebraic perspex is a generalization of matrices, it provides the most general representation for all of the interpretations of a perspex. The algebraic perspex can be used to describe arbitrary sets of coordinates. The remaining three interpretations of the perspex are all related to square matrices and operate in a Euclidean model of projective space-time, called perspex space. Perspex space differs from the usual Euclidean model of projective space in that it contains the point at nullity. It is argued that the point at nullity is necessary for a consistent account of perspective in top-down vision. Second, the geometric perspex is a simplex in perspex space. It can be used as a primitive building block for shapes, or as a way of recording landmarks on shapes. Third, the transformational perspex describes linear transformations in perspex space that provide the affine and perspective transformations in space-time. It can be used to match a prototype shape to an image, even in so called 'accidental' views where the depth of an object disappears from view, or an object stays in the same place across time. Fourth, the parametric perspex describes the geometric and transformational perspexes in terms of parameters that are related to everyday English descriptions. The parametric perspex can be used to obtain both continuous and categorical perception of objects. The paper ends with a discussion of issues related to using a perspex to describe logic.

Canonical description of the perspective projections

A unique parameterization of the perspective projections in all whole-numbered dimensions is reported. The algorithm for generating a perspective transformation from parameters and for recovering parameters from a transformation is a modification of the Givens orthogonalization algorithm. The algorithm for recovering a perspective transformation from a perspective projection is a modification of Roberts' classical algorithm. Both algorithms have been implemented in Pop-11 with call-out to the NAG Fortran libraries. Preliminary monte-carlo tests show that the transformation algorithm is highly accurate, but that the projection algorithm cannot recover magnitude and shear parameters accurately. However, there is reason to believe that the projection algorithm might improve significantly with the use of many corresponding points, or with multiple perspective views of an object. Previous parameterizations of the perspective transformations in the computer graphics and computer vision literature are discussed.

POP-11 comes of age: the advancement of an AI programming language

In 1989, the computer programming language POP-11 is 21 years old. This book looks at the reasons behind its invention, and traces its rise from an experimental language to a major AI language, playing a major part in many innovating projects. There is a chapter on the inventor of the language, Robin Popplestone, and a discussion of the applications of POP-11 in a variety of areas. The efficiency of AI programming is covered, along with a comparison between POP-11 and other programming languages. The book concludes by reviewing the standardization of POP-11 into POP91.

Hardware development of the Yorick series of active vision systems

This paper presents a review of the design and development of the Yorick series of active stereo camera platforms and their integration into real-time closed loop active vision systems, whose applications span surveillance, navigation of autonomously guided vehicles (AGVs), and inspection tasks for teleoperation, including immersive visual telepresence. The mechatronic approach adopted for the design of the first system, including head/eye platform, local controller, vision engine, gaze controller and system integration, proved to be very successful. The design team comprised researchers with experience in parallel computing, robot control, mechanical design and machine vision. The success of the project has generated sufficient interest to sanction a number of revisions of the original head design, including the design of a lightweight compact head for use on a robot arm, and the further development of a robot head to look specifically at increasing visual resolution for visual telepresence. The controller and vision processing engines have also been upgraded, to include the control of robot heads on mobile platforms and control of vergence through tracking of an operator's eye movement. This paper details the hardware development of the different active vision/telepresence systems.

Driving saccade to pursuit using image motion

Within the context of active vision, scant attention has been paid to the execution of motion saccades—rapid re-adjustments of the direction of gaze to attend to moving objects. In this paper we first develop a methodology for, and give real-time demonstrations of, the use of motion detection and segmentation processes to initiate capture saccades towards a moving object. The saccade is driven by both position and velocity of the moving target under the assumption of constant target velocity, using prediction to overcome the delay introduced by visual processing. We next demonstrate the use of a first order approximation to the segmented motion field to compute bounds on the time-to-contact in the presence of looming motion. If the bound falls below a safe limit, a panic saccade is fired, moving the camera away from the approaching object. We then describe the use of image motion to realize smooth pursuit, tracking using velocity information alone, where the camera is moved so as to null a single constant image motion fitted within a central image region. Finally, we glue together capture saccades with smooth pursuit, thus effecting changes in both what is being attended to and how it is being attended to. To couple the different visual activities of waiting, saccading, pursuing and panicking, we use a finite state machine which provides inherent robustness outside of visual processing and provides a means of making repeated exploration. We demonstrate in repeated trials that the transition from saccadic motion to tracking is more likely to succeed using position and velocity control, than when using position alone.

A modular head/eye platform for real-time reactive vision

This paper describes the design, implementation and testing of a high speed controlled stereo “head/eye” platform which facilitates the rapid redirection of gaze in response to visual input. It details the mechanical device, which is based around geared DC motors, and describes hardware aspects of the controller and vision system, which are implemented on a reconfigurable network of general purpose parallel processors. The servo-controller is described in detail and higher level gaze and vision constructs outlined. The paper gives performance figures gained both from mechanical tests on the platform alone, and from closed loop tests on the entire system using visual feedback from a feature detector.

Robot free will

We introduce the perspex machine which unifies projective geometry and Turing computation and results in a supra-Turing machine. We show two ways in which the perspex machine unifies symbolic and non-symbolic AI. Firstly, we describe concrete geometrical models that map perspexes onto neural networks, some of which perform only symbolic operations. Secondly, we describe an abstract continuum of perspex logics that includes both symbolic logics and a new class of continuous logics. We argue that an axiom in symbolic logic can be the conclusion of a perspex theorem. That is, the atoms of symbolic logic can be the conclusions of sub-atomic theorems. We argue that perspex space can be mapped onto the spacetime of the universe we inhabit. This allows us to discuss how a robot might be conscious, feel, and have free will in a deterministic, or semi-deterministic, universe. We ground the reality of our universe in existence. On a theistic point, we argue that preordination and free will are compatible. On a theological point, we argue that it is not heretical for us to give robots free will. Finally, we give a pragmatic warning as to the double-edged risks of creating robots that do, or alternatively do not, have free will.

Perspex machine X: software development

The Perspex Machine arose from the unification of computation with geometry. We now report significant redevelopment of both a partial C compiler that generates perspex programs and of a Graphical User Interface (GUI). The compiler is constructed with standard compiler-generator tools and produces both an explicit parse tree for C and an Abstract Syntax Tree (AST) that is better suited to code generation. The GUI uses a hash table and a simpler software architecture to achieve an order of magnitude speed up in processing and, consequently, an order of magnitude increase in the number of perspexes that can be manipulated in real time (now 6,000). Two perspex-machine simulators are provided, one using trans-floating-point arithmetic and the other using transrational arithmetic. All of the software described here is available on the world wide web. The compiler generates code in the neural model of the perspex. At each branch point it uses a jumper to return control to the main fibre. This has the effect of pruning out an exponentially increasing number of branching fibres, thereby greatly increasing the efficiency of perspex programs as measured by the number of neurons required to implement an algorithm. The jumpers are placed at unit distance from the main fibre and form a geometrical structure analogous to a myelin sheath in a biological neuron. Both the perspex jumper-sheath and the biological myelin-sheath share the computational function of preventing cross-over of signals to neurons that lie close to an axon. This is an example of convergence driven by similar geometrical and computational constraints in perspex and biological neurons.