We explore two approaches to image segmentation. One approach uses watershed algorithm that has a tendency to overdo the segmentation. We can extract desired features and eliminate noises via persistent homology from topological data analysis. The other approach uses wavelet transform. Wavelet transform detects change in color intensity of the pixels on the boundaries of objects, which leads us to obtain segmented images. We then discuss properties of these two methods including some advantages, disadvantages and algorithmic efficiency.