This paper presents a deformable pyramid transform (DPT) with shift-invariance, steerability, and scalability. This DPT is extended from a numerical steerable pyramid transform (SPT). We take each steerable basis filter of the SPT as the kernel. For each kernel, we employ the singular value decomposition (SVD) approach to construct scalable basis filters and their corresponding interpolation functions. These scalable basis filters are used as analysis filters of the DPT. Its synthesis filters are then theoretically derived under the constraint of perfect reconstruction for analysis and synthesis filters. In addition, we theoretically derive the interpolation function for steerability, and quantitatively analyze the relationship between the number of scalable basis filters and the reconstruction performance. Numerical simulations demonstrate that the proposed scalable basis filters satisfy the constraint of perfect reconstruction. Also, it is observed that merely using half of the number of scalable basis filters can approximate the optimum reconstruction performance at a cost of reconstruction error within 1 dB. Keywords: