3D Height / Width. Building upon the height and width measurements taken in the image plane, height and width measurements are now taken incorporating known camera geometry. This method allows known camera positions relative to object positions in the scene to compute very accurate object height and width measurements. These measurements are invariant to perspective or affine distortion, but not to occlusion. It is important to note, that although the measurements themselves are invariant to 3D rotation within the scene, providing accurate measurements of the object irrespective of their position, this rotation will alter the size of the object under observation. For example, a car viewed side on will be a different width to a car viewed head on. This change can be compensated for within the model created, as the centroid positions will consider these variations. However, this may reduce the accuracy of the final classification, as some classes may overlap. This overlap may mar the decision boundaries. 5.1.2.2. Moments Region moment representations interpret a normalised graylevel image function as a probability density of a 2D random variable. Properties of this random variable can be described using statistical characteristics moments [21]. Moments allow an object to be described using standard statistics, for example, the objects area ( m00 ). The use of several statistical descriptions of an object allows a specific object's type (classification) to be postulated. This system has been used to great effect in object and letter classification by Xxxxxxx and Suk [23]. In digitised images, moments are created such that: ∞ mpq = ∑ i=−∞ ∞ ∑ j=−∞ i p jq f i , j (5.1) Where i, j are the pixel coordinates and p,q describe the moments to create (for example, to create m00 , p and q = 0). It is advantageous for moments to be as invariant as possible as in Section 5.1.2.1., where the heights to width measurements are made invariant to perspective projection. Invariance in moments allows for a more robust and flexible object representation. Translation invariance (i.e. moments that appear the same at any position within the image) can be achieved if image central moments are used [22], through the generalised formula: ∞ μ pq = ∑ i=−∞ ∞ ∑ j=−∞
3D Height / Width. Encouraged by the noninvariant model of height and width (size), an invariant form was created using known camera geometry to increase measurement accuracy and overcome the problems of distance, or perspective, within the data files. This model used the same decisionboundary creation schemes as the noninvariant model, and matched in the same manner, but scores over the noninvariant model in the accuracy of the measurements returned. Although this invariant model gives better results than its noninvariant form (as can be seen from the results obtained), the classification accuracy is not high enough for outright object class to be determined based on this technique. This is mainly due to the problems of 3D rotation within the invariant model, for although it is invariant to scale, the measurements returned are nonlinear (i.e. as an object turns, its class remains the same, but its size alters nonlinearly). This type of sizebased model cannot easily cope with this problem. The model used can claim to reduce the effects of 3D rotation, which is done using Mahalanobis distance, which takes the distribution (alterations) in rotation into account for each object. Unfortunately, this is obviously not sufficient for the task, however, based on the results listed in [85].
