This paper first shows that REC, the family of recognizable picture languages in Giammarresi and Restivo (1991), is equal to the family of picture languages accepted by two-dimensional on-line tessellation acceptors in Inoue and Nakamura (1977). By using this result, we then solve open problems in Giammarresi and Restivo (1991), and show that (i) REC is not closed under complementation, and (ii) REC properly contains the family of picture languages accepted by two-dimensional nondeterministic finite automata even over a one letter alphabet.