In this thesis, an object detection system based on omnidirectional camera which has the advantages of detecting a large view-field is introduced. Initially, the traditional camera approach that uses sliding windows and Histogram of Gradients (HOG) features is adopted. Later on, how the feature extraction step of the conventional approach should be modified is described. The aim is an efficient and mathematically correct use of HOG features in omnidirectional images. Main steps are conversion of gradient orientations to compose an omnidirectional sliding window and modification of gradient magnitudes by means of Riemannian metric. Owing to the proposed methods, object detection process can be performed on the omnidirectional images without converting them to panoramic or perspective image. Experiments that are conducted with both synthetic and real images compare the proposed approach with regular (unmodified) HOG computation on both omnidirectional and panoramic images. Results show that the performance of detection has been improved by using the proposed method.