A novel scheme for image segmentation is presented. An image segmentation criterion is proposed that groups similar pixels together to form regions. This criterion is formulated as a cost function. This cost function is minimized by using gradient-descent methods, which lead to a curve evolution equation that segments the image into multiple homogenous regions. Homogeneity is specified through a pixel-to-pixel similarity measure, which is defined by the user and can be adaptive based on the current application. To improve the performance of the system, an edge function is also used to adjust the speed of the competing curves. The proposed method can be easily applied to vector valued images such as texture and color images without a significant addition to computational complexity.