Fractal image compression is one of the most promising techniques for image compression due to advantages such as resolution independence and fast decompression. It exploits the fact that natural scenes present self-similarity to remove redundancy and obtain high compression rates with smaller quality degradation compared to traditional compression methods. The main drawback of fractal compression is its computationally intensive encoding process, due to the need for searching regions with high similarity in the image. Several approaches have been developed to reduce the computational cost to locate similar regions. In this work, we propose a method based on robust feature descriptors to speed up the encoding time. The use of robust features provides more discriminative and representative information for regions of the image. When the regions are better represented, the search for similar parts of the image can be reduced to focus only on the most likely matching candidates, which leads to reduction on the computational time. Our experimental results show that the use of robust feature descriptors reduces the encoding time while keeping high compression rates and reconstruction quality.