In high-performance computing (HPC) environments, particularly in synchrotron radiation facilities, vast amounts of X-ray images are generated. Processing large-scale X-ray Computed Tomography (X-CT) datasets presents significant computational and storage challenges due to their high dimensionality and data volume. Traditional approaches often require extensive storage capacity and high transmission bandwidth, limiting real-time processing capabilities and workflow efficiency. To address these constraints, we introduce a region-of-interest (ROI)-driven extraction framework (ROIX-Comp) that intelligently compresses X-CT data by identifying and retaining only essential features. Our work reduces data volume while preserving critical information for downstream processing tasks. At pre-processing stage, we utilize error-bounded quantization to reduce the amount of data to be processed and therefore improve computational efficiencies. At the compression stage, our methodology combines object extraction with multiple state-of-the-art lossless and lossy compressors, resulting in significantly improved compression ratios. We evaluated this framework against seven X-CT datasets and observed a relative compression ratio improvement of 12.34x compared to the standard compression.