3D modeling of the real-world objects is one of the basic problems in the field of computer vision. Not only this may be a goal in itself but also could be the prelude to solve other problems. Theexisting methods typically employ depth sensors such as laser rang-finders or stereo cameras toextract surface points of objects. The set of extracted points is then called a point cloud. Due to thenature of the sensors, to extract the complete point cloud the sensor should be used at differentlocations and angles. In this way multiple partial point clouds are obtained each of which in adifferent coordinate system. The problem of bringing all partial point clouds into a commoncoordinate system which is known as registration can be done by having at least threecorrespondences for each pair. Since f inding exact correspondences may not be possible, manycorrespondences are computed at first and then RANSAC algorithm is used to find a near optimaltransformation. To find the correspondences, local 3d descriptors which are computed for each point are used to describe the points around it. By comparing alldescriptors of a pair of clouds we are able to find the correspondences. However the existingdescriptors have some problems such as high computational and memory complexities and not beingscale invariant. To tackle some of these problems a new covariance matrix–based local descriptor isintroduced in this thesis. Besides having well-defined divergence measures with good theoreticalfeatures covariance matrices have some other good features like high descriptivity, non–parametricityand low memory requirement which motivate us to use them as 3d descriptors. In addition to introducing this new descriptor, this thesis also describes a new method for determining the points involved in thecomputation of an instance of the introduced descriptor which makes it invariant to scale changes. Experiments show that the descriptor has a good descriptivity and really low computationalcomplexity. Also it worths noting that the descriptor together with the neighbor determining method iscompletely invariant to scale changes, a property which none of previous descriptors have.