Estimation of distances in virtual environments using size constancy

It is reported in the literature that distances from the observer are underestimated more in virtual environments (VEs) than in physical world conditions. On the other hand estimation of size in VEs is quite accurate and follows a size-constancy law when rich cues are present. This study investigates how estimation of distance in a CAVETM environment is affected by poor and rich cue conditions, subject experience, and environmental learning when the position of the objects is estimated using an experimental paradigm that exploits size constancy. A group of 18 healthy participants was asked to move a virtual sphere controlled using the wand joystick to the position where they thought a previously-displayed virtual cube (stimulus) had appeared. Real-size physical models of the virtual objects were also presented to the participants as a reference of real physical distance during the trials. An accurate estimation of distance implied that the participants assessed the relative size of sphere and cube correctly. The cube appeared at depths between 0.6 m and 3 m, measured along the depth direction of the CAVE. The task was carried out in two environments: a poor cue one with limited background cues, and a rich cue one with textured background surfaces. It was found that distances were underestimated in both poor and rich cue conditions, with greater underestimation in the poor cue environment. The analysis also indicated that factors such as subject experience and environmental learning were not influential. However, least square fitting of Stevens’ power law indicated a high degree of accuracy during the estimation of object locations. This accuracy was higher than in other studies which were not based on a size-estimation paradigm. Thus as indirect result, this study appears to show that accuracy when estimating egocentric distances may be increased using an experimental method that provides information on the relative size of the objects used.

Time series multistep-ahead predictability estimation and ranking

A predictability index was defined as the ratio of the variance of the optimal prediction to the variance of the original time series by Granger and Anderson (1976) and Bhansali (1989). A new simplified algorithm for estimating the predictability index is introduced and the new estimator is shown to be a simple and effective tool in applications of predictability ranking and as an aid in the preliminary analysis of time series. The relationship between the predictability index and the position of the poles and lag p of a time series which can be modelled as an AR(p) model are also investigated. The effectiveness of the algorithm is demonstrated using numerical examples including an application to stock prices.