Image compression techniques are presented in this paper which can be used for storage and transmission of digital lossy images. It is mostly important in both multimedia and medical field to store huge database and data transfer. Medical images are used for diagnosis purposes. So, vector quantization is a novel method for lossy image compression that includes codebook design, encoding and decoding stages. Here, we have applied different lossy compression techniques like VQ-LBG (Vector quantization- Linde, Buzo and Gray algorithm), DWT-MSVQ (Discrete wavelet transform-Multistage Vector quantization), FCM (Fuzzy c-means clustering) and GIFP-FCM (Generalized improved fuzzy partitions-FCM) methods on different medical images to measure the qualities of compression. GIFP-FCM is an extension of classical FCM and IFP-FCM (Improved fuzzy partitions FCM) algorithm with a purpose to reward hard membership degree. The presentation is assessed based on the effectiveness of grouping output. In this method, a new objective function is reformulated and minimized so that there is a smooth transition from fuzzy to crisp mode. It is fast, easy to implement and has rapid convergence. Thus, the obtained results show that GIFP-FCM algorithm gives better PSNR performance, high CR (compression ratio), less MSE (Mean square error) and less distortion as compared to other above used methods indicating better image compression.