This paper proposes a new shape adaptive integer wavelet transform (SAIWT) based progressive transmission coding scheme for 2-D and 3-D brain MRI. This scheme consists of: (a) extraction of shape information (mask) by morphological operations; (b) 2D/3D separable biorthogonal 9-7 SAIWT; (c) intraband wavelet encoding of the foreground object. This object based coding greatly improves both overall progressive transmission performance and lossless compression; (d) entropy coding of resulting bit stream and differential coding of the boundary of binary mask. The performance of shape adaptive scheme (both 2D and 3D) is superior to the conventional rectangular based schemes at all bit rates.