Object and texture recognition are two important subjects in computer vision. An efficient and fast algorithm to compute a short and efficient feature vector for classification of images is crucial for smart video surveillance systems. In this thesis, feature extraction methods for object and texture classification are investigated, compared and developed. A method for object classification based on shape characteristics is developed. Object silhouettes are extracted from videos by using the background subtraction method. Contour of the objects are obtained from these silhouettes and this 2-D contour signals are transformed into 1-D signals by using a type of radial transformation. Discrete cosine transformation is used to acquire the frequency characteristics of these signals and a support vector machine (SVM) is employed for classification of objects according to this frequency information. This method is implemented and integrated into a real time system together with object tracking. For texture recognition problem, we defined a new computationally efficient operator forming a semigroup on real numbers. The new operator does not require any multiplications. The codifference matrix based on the new operator is defined and an image descriptor using the codifference matrix is developed. Texture recognition and license plate identification examples based on the new descriptor are presented. We compared our method with regular covariance matrix method. Our method has lower computational complexity and it is experimentally shown that it performs as well as the regular covariance method.