Image and video sensors are increasingly being deployed in complex systems due to the rich process information that these sensors can capture. As a result, image data play an important role in process monitoring and control in different application domains such as manufacturing processes, food industries, medical decision-making, and structural health monitoring. Existing process monitoring techniques fail to fully utilize the information of color images due to their complex data characteristics including the high-dimensionality and correlation structure (i.e., temporal, spatial and spectral correlation). This paper proposes a new image-based process monitoring approach that is capable of handling both grayscale and color images. The proposed approach models the high-dimensional structure of the image data with tensors and employs low-rank tensor decomposition techniques to extract important monitoring features monitored using multivariate control charts. In addition, this paper shows the analytical relationships between different low-rank tensor decomposition methods. The performance of the proposed method in quick detection of process changes is evaluated and compared with existing methods through extensive simulations and a case study in a steel tube manufacturing process. Note to Practitioners - This paper, motivated by the problem of combustion monitoring in steel tube manufacturing, focuses on the development of effective methods for process monitoring based on image data. Existing process monitoring techniques cannot fully utilize the information of color images due to the high-dimensionality and complex correlation structure of such data. This paper addresses this problem by extracting essential monitoring features, while considering the spatial and spectral correlation of color images. This is accomplished by using various low-rank tensor decomposition methods along with multivariate control charts. The proposed approach can lead to a computer-aided online monitoring system for automatic detection of out-of-control situations in a process. Using simulation, the performance of the developed methods is compared under various scenarios. This can provide practitioners with useful guidelines for selecting an appropriate method for image-based process monitoring. In future research, we will study the development of image-based fault diagnosis techniques that can be integrated with the process monitoring approaches proposed in this paper.