The Riemannian Geometry Theory of Visually-Guided Movement Accounts for Afterimage Illusions and Size Constancy.

This discussion paper supplements our two theoretical contributions previously published in this journal on the geometric nature of visual space. We first show here how our Riemannian formulation explains the recent experimental finding (published in this special issue on size constancy) that, contrary to conclusions from past work, vergence does not affect perceived size. We then turn to afterimage experiments connected to that work.

A Riemannian Geometry Theory of Synergy Selection for Visually-Guided Movement.

Bringing together a Riemannian geometry account of visual space with a complementary account of human movement synergies we present a neurally-feasible computational formulation of visuomotor task performance. This cohesive geometric theory addresses inherent nonlinear complications underlying the match between a visual goal and an optimal action to achieve that goal: (i) the warped geometry of visual space causes the position, size, outline, curvature, velocity and acceleration of images to change with changes in the place and orientation of the head, (ii) the relationship between head place and body posture is ill-defined, and (iii) mass-inertia loads on muscles vary with body configuration and affect the planning of minimum-effort movement. We describe a partitioned visuospatial memory consisting of the warped posture-and-place-encoded images of the environment, including images of visible body parts.

A Riemannian Geometry Theory of Three-Dimensional Binocular Visual Perception.

We present a Riemannian geometry theory to examine the systematically warped geometry of perceived visual space attributable to the size-distance relationship of retinal images associated with the optics of the human eye. Starting with the notion of a vector field of retinal image features over cortical hypercolumns endowed with a metric compatible with that size-distance relationship, we use Riemannian geometry to construct a place-encoded theory of spatial representation within the human visual system. The theory draws on the concepts of geodesic spray fields, covariant derivatives, geodesics, Christoffel symbols, curvature tensors, vector bundles and fibre bundles to produce a neurally-feasible geometric theory of visuospatial memory.

A Riemannian geometry theory of human movement: The geodesic synergy hypothesis.

Mass-inertia loads on muscles change with posture and with changing mechanical interactions between the body and the environment. The nervous system must anticipate changing mass-inertia loads, especially during fast multi-joint coordinated movements. Riemannian geometry provides a mathematical framework for movement planning that takes these inertial interactions into account.

On theory of motor synergies.

Recently Latash, Scholz, and Schöner (2007) proposed a new view of motor synergies which stresses the idea that the nervous system does not seek a unique solution to eliminate redundant degrees of freedom but rather uses redundant sets of elemental variables that each correct for errors in the other to achieve a performance goal. This is an attractive concept because the resulting flexibility in the synergy also provides for performance stability. But although Latash et al.

Motor maps and synergies.

Consider the process of raising and lowering the arm in the sagittal plane. Different parts of different muscles operate over different sectors of the angular range. How and why does the nervous system implement this differential muscle activation according to joint angle? We contend that such control depends on the adaptive formation of motor maps.

An overview of adaptive model theory: solving the problems of redundancy, resources, and nonlinear interactions in human movement control.

Adaptive model theory (AMT) is a computational theory that addresses the difficult control problem posed by the musculoskeletal system in interaction with the environment. It proposes that the nervous system creates motor maps and task-dependent synergies to solve the problems of redundancy and limited central resources. These lead to the adaptive formation of task-dependent feedback/feedforward controllers able to generate stable, noninteractive control and render nonlinear interactions unobservable in sensory-motor relationships.

A new view on visuomotor channels: the case of the disappearing dynamics.

A considerable body of kinematic data supports the proposal that independent visuomotor channels are involved in the control of the transport and grip components of reach and grasp. These channels are seen as having separate perceptual inputs, outputs and internal processing and are thought by some to correspond to independent neuroanatomical pathways. The idea that different groups of muscles and biomechanical structures can be controlled independently is attractive, but this kinematically-inspired hypothesis fails to take into account the complexity of the dynamic relationships and their interactions within the neuromusculoskeletal system.

Anisotropic tracking: evidence for automatic synergy formation in a bimanual task.

Investigation of interlimb synergy has become synonymous with the study of coordination dynamics and is largely confined to periodic movement. Based on a computational approach this paper demonstrates a method of investigating the formation of a novel synergy in the context of stochastic, spatially asymmetric movements. Nine right-handed participants performed a two degrees of freedom (2D) "etch-a-sketch" tracking task where the right hand controlled the horizontal position of the response cursor on the display while the left hand controlled the vertical position.