Efficiently processing medical images, such as whole slide images in digital pathology, is essential for timely diagnosing high-risk diseases. However, this demands advanced computing infrastructure, e.g., GPU servers for deep learning inferencing, and local processing is time-consuming and costly. Besides, privacy concerns further complicate the employment of remote cloud infrastructures. While previous research has explored privacy and security-aware workflow scheduling in hybrid clouds for distributed processing, privacy-preserving data splitting, optimizing the service allocation of outsourcing computation on split data to the cloud, and privacy evaluation for large medical images still need to be addressed. This study focuses on tailoring a virtual infrastructure within a hybrid cloud environment and scheduling the image processing services while preserving privacy. We aim to minimize the use of untrusted nodes, lower monetary costs, and reduce execution time under privacy, budget, and deadline requirements. We consider a two-phase solution and develop 1) a privacy-preserving data splitting algorithm and 2) a greedy Pareto front-based algorithm for optimizing the service allocation. We conducted experiments with real and simulated data to validate and compare our method with a baseline. The results show that our privacy mechanism design outperforms the baseline regarding the average lower band on individual privacy and information gain for privacy evaluation. In addition, our approach can obtain various Pareto optimal-based allocations with users' preferences on the maximum number of untrusted nodes, budget, and time threshold. Our solutions often dominate the baseline's solution and are superior on a tight budget. Specifically, our approach has been ahead of baseline, up to 85.2% and 6.8% in terms of the total financial and time costs, respectively.