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The recent development on semiconductor process and design technologies enables multi-core processors to become a dominant market trend in desk-top PCs as well as high end mobile devices. At the same time, the increasing popularity of high quality digital contents processing makes processors to quip with dedicated instructions based on sub-word parallelism in order to process streaming data. This paper presents a way of optimizations of 2D convolution operator, a widely used technique in image and signal processing applications, on speed in Intel multi-core processors. Two optimization techniques are discussed in detail. One is the streaming SIMD (Single Instruction Multiple Data) extension (SSE) technology, available in Intel processors, for data parallelism. The other is the Intel TBB (Threading Building Block) run-time library to exploit parallelism in task level. As a result, this paper can investigate the advantage of two different parallelisms, both data and task, concurrently. For the performance evaluation, we implemented Sobel operator using SSE and TBB with different combinations and compared their processing speeds. The results show that both technologies have a significant effect on the performance and the processing speed can be greatly improved when using two technologies at the same time.