Adaptive Color Quantization (ACQ) as described here is one method of color image compression employed for image storage and display in low cost monitors. Due to the nature of the palette based mapping employed in ACQ, it is prone to large errors due to noises introduced in transmission or additional lossy compression. This paper proposes a robust method of ACQ using a three-dimensional Self Organizing Map (3D SOM), which is tolerant to noises. The robustness of the 3D SOM is due to the property of such maps to cluster the color vectors in a topological manner. An efficient parallel architecture based on SIMD structure and parallel winner determination scheme, is presented for the implementation of the 3D SOM. The VLSI area-time efficiency of this parallel architecture over the current implementations is also established.