Table 1.

Tabulation of previous results relating to texture constancy which are all explained by the brain's ability to access specific attributes of the invariant surface descriptor s(x) through the temporal gradient $s\prime \left(\overline{x}\right)v\left(t\right)$.

Study and main condition	Task	Movement generation		Quantities available				Constancy
				s′(x(t))	$s\left(\overline{x}\right)\left(t\right)$	v(t)	$\overline{v}\left(t\right)$		Case
Katz (1925/1989), natural surfaces. Lederman (1981) gratings of constant periodicity; bare finger.	Roughness estimation	Self		yes	yes	yes	yes	yes	(1)
		External		yes	yes	no	yes
Lamb (1983), Meftah et al. (2000), raised dots constant periodicity, bare finger.	Spatial period discrimination Roughness estimation	Self		yes	yes	yes	yes	yes	(2)
		External		yes	yes	no	yes
Hughes et al. (2007), raised dots with spatial period gradient, bare finger.	Spatial period gradient discrimination	Self		yes	yes	yes	yes	yes	(3)
Lawrence et al. (2007), gratings of constant periodicity; bare finger, rigid probe.	Roughness estimation	Self	Finger	yes	yes	yes	yes	yes	(4)
			Probe	yes	no	yes	no
Wiertlewski et al. (2011a), natural surfaces, bare finger via causality inversion.	Identification and spatial period discrimination	Self		yes	no	yes	no	yes	(5)
		External		yes	no	no	no	no	(6)
Yoshioka et al. (2011) natural surfaces; bare finger, rigid probe	Roughness estimation	Self	Finger	yes	yes	yes	yes
			Probe	yes	no	yes	no	yes	(7)
		External	Finger	yes	yes	no	yes
			Probe	yes	no	no	no	no	(8)
Libouton et al. (2012) natural surfaces; de-afferented extremities	Roughness estimation	Self		yes	no	yes	no	yes	(9)

If v(t) is inaccessible, constancy breaks down (cases 6, 8).