In this dissertation, the methods of protection and authentication for digital images are presented. In the study of fragile image authentication, the method that can thwart the counterfeit attack is proposed in Chapter 2, and we analyze this method in order to prove the effect. In the study of semi-fragile image authentication, two image authentication methods with digital signature-based and digital watermark-based are presented in Chapter 3 and Chapter 4 respectively. These two methods can improve the disadvantages of related works, and the main contributions are: (1) can adjust the fragile degree by assigning the least authenticable bound of image and (2) the related theorems about the proposed methods are analyzed completely. Finally, a new issue and solution about semi-fragile image authentication are presented in Chapter 5. The main contributions of this method are: (1) only the spatial domain is adopted during feature generation and verification, making domain transformation process is unnecessary, (2) more reasonable non-malicious manipulated images (JPEG, JPEG2000 compressed and scaled images) than related studies can be authenticated, achieving a good trade-off of image authentication between fragile and robust under practical image processing, and (3) non-malicious manipulation is clearly defined to meet closely the requirements of sending them over the Internet or storing images.