This paper presents a scheme for secure coding of arbitrarily-shaped visual objects. Called SecST-SPIHT, it employs SPIHT based coding along with selective encryption for efficient, secure storage and transmission of visual object shape and texture. The selective encryption utilizes a novel bit classification scheme which ensures protection of the entire code by encrypting only a small number of bits (less than 5% for securing shape and texture, and less than 0.5% for just the texture). The encryption is performed in the compressed domain and does not affect the rate-distortion performance of the coder. A parameter allows control over the strength of the encryption versus required processing overhead. The scheme can be employed in a privacy protected surveillance system, whereby visual objects of human subjects are encrypted so that the content is only available to certain entities, such as persons of authority, possessing the correct decryption key.