1 Introduction Ever since the pioneering work of Weber (1834/1978, eg see pages 105^107) and Fechner (1860/1966, pages 176 ^ 197), psychophysicists have investigated the precision and accuracy of human observers' visual perceptions of distance. In many of these investigations, researchers have examined how observers perceive distances between pairs of environmental locations. These studies have revealed that observers apparently per- ceive distances in depth in a manner that is qualitatively different from how they perceive horizontal distances in a frontoparallel plane öin particular, it has been fre- quently found that distances in depth are perceptually compressed in relation to those that occur in the frontoparallel plane (eg see Beusmans 1998; Gilinsky 1951; Harway 1963; Loomis et al 1992; Loomis and Philbeck 1999; Norman et al 1996; Wagner 1985; Wu et al 2004). One can learn even more by studying how human observers perceive the spatial relationships between triplets of environmental points (eg Battro et al 1976; Blank 1958; Higashiyama 1981; Koenderink et al 2000). In an intriguing experiment conducted by Battro et al (pages 20^ 21), observers estimated the distances contained within large outdoor triangles. They concluded from their experiment (see their table 9) that for 15 m triangles (the length of the side of the triangle opposite the observer was15 m), five of their ten observers' judgments were consistent with a hyperbolic geom- etry, while the remaining five observers' judgments were consistent with an elliptic geometry. In other words, none of the observers'estimates was consistent with ordinary Euclidean geometry öall of the observers perceived spatial relationships that indicated that their visual space was curved, either analogous to the surface of a horse's saddle (hyperbolic geometry) or to the surface of a sphere (elliptic geometry). These findings are remarkable and thought-provoking. However interesting the basic finding, it is impossible to learn anything more about Battro et al's results, because no actual data concerning this experiment were ever published in the 1976 article. All of the ten observ- ers in the 15 m condition ostensibly exhibited significant perceptual distortions, but we do not know the precise nature or the magnitude of the distortions that were obtained. Were they large in magnitude? Were they small, but statistically significant? The perception of distances and spatial relationships in natural outdoor environments Perception, 2005, volume 34, pages 1315 ^ 1324 J Farley Norman, Charles E Crabtree, Anna Marie Clayton, Hideko F Norman Department of Psychology, Western Kentucky University, Bowling Green, KY 42101-3576, USA; e-mail: Farley.Norman@wku.edu Received 1 July 2004, in revised form 2 March 2005; published online 28 October 2005 Abstract. The ability of observers to perceive distances and spatial relationships in outdoor environments was investigated in two experiments. In experiment 1, the observers adjusted trian- gular configurations to appear equilateral, while in experiment 2, they adjusted the depth of triangles to match their base width. The results of both experiments revealed that there are large individual differences in how observers perceive distances in outdoor settings. The observers' judg- ments were greatly affected by the particular task they were asked to perform. The observers who had shown no evidence of perceptual distortions in experiment 1 (with binocular vision) demonstrated large perceptual distortions in experiment 2 when the task was changed to match distances in depth to frontal distances perpendicular to the observers' line of sight. Considered as a whole, the results indicate that there is no single relationship between physical and perceived space that is consistent with observers' judgments of distances in ordinary outdoor contexts. DOI:10.1068/p5304