T. Heap and D. Hogg. Extending the point distribution model using polar coordinates. Image and Vision Computing, 14(8):589--599, 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....both the linear and polynomial regression models fail. The MLPPDM succeeds in generating a specific and parsimonious model with 30 examples, but does not succeed after training with 10 examples. Thus the MLPPDM appears to outperform the PRPDM for modelling non linear shape variation. Heap and Hogg [6] describe using polar co ordinates for sub parts of a PDM, allowing them to rotate. Although potentially useful, this is not as general a model as the MLP based approach described here. An MLPPDM is computationally inexpensive to use, but takes significantly longer to train than a linear or ....

T. Heap and D. Hogg, "Extending the Point Distribution Model Using Polar Co-ordinates", Internal Report 95 5, Computer Studies, Leeds University (1995).

....to linearise shape changes from the mean shape, which may in reality be non linear. By reparametrising the shapes it may be possi 92 ble to ensure that the shape changes are closer to a linear model. A similar effect is apparent in the #Cartesian Polar Hybrid# PDM described by Heap and Hogg [55] where the choice of shape representation can signi#cantly improve the resulting model. Another way of looking at the problem is to consider the initial training set to lie within a lower dimensional, constrained shape space, within the original shape vector space. This space is de#ned by the ....

A J Heap and D C Hogg. Extending the Point Distribution Model using polar coordinates. In Proc. CAIP, pages 130#137, Prague, Czech Republic, September 1995.

....training input are of comparable units. However, when converting to polar coordinates, we change from distance (x,y) pairs to pairs of displacement and angle, r, which are not comparable. To compensate for this, we use the relation s = r , where s is the arc length of an angle at radius r [11]. This allows the use of arc lengths, which are comparable with displacements, instead of angles. We used a training set of 120 examples, flipped around the principal axis in order to invoke symmetry and double the number of examples [12] The mean shape for this model can be seen in Figure 3, ....

A.J. Heap and D.C. Hogg. Extending the point distribution model using polar coordinates. Image and Vision Computing, pages 589--599, 1996.

....both the linear and polynomial regression models fail. The MLPPDM succeeds in generating a specific and parsimonious model with 30 examples, but does not succeed after training with 10 examples. Thus the MLPPDM appears to outperform the PRPDM for modelling non linear shape variation. Heap and Hogg [6] describe using polar co ordinates for sub parts of a PDM, allowing them to rotate. Although potentially useful, this is not as general a model as the MLP based approach described here. An MLPPDM is computationally inexpensive to use, but takes significantly longer to train than a linear or ....

T. Heap and D. Hogg, "Extending the Point Distribution Model Using Polar Co-ordinates", Internal Report 95 5, Computer Studies, Leeds University (1995).

....when invalid combinations of deformations are used. British Machine Vision Conference 2 Attempts have been made to combat this problem. Sozou et al. s Polynomial Regression PDM [9] allows landmark points to move along combinations of polynomial paths. Heap and Hogg s Cartesian Polar Hybrid PDM [6] makes use of polar coordinates to model bending deformations more accurately. Sozou et al. [10] have also investigated using a multi layer perceptron to provide a non linear mapping from shape parameters to shape. All these approaches give some improvement over the linear PDM, but they have their ....

.... not compact because the dimensionality is increased, and not specific because invalid shapes can be produced via an invalid combination of linear deformations (see Figure 4 for examples) There are various techniques one can use to transform the shape space in such a way as to linearise the VSR [9, 10, 6]. In these approaches there is always a notion of a base shape (usually the mean shape) and a fixed number of independent modes of variation, valid over a fixed, continuous range. However, in some cases the VSR is not linearisable in a simple manner. A VSR can in theory have an arbitrary topology ....

A.J. Heap and D.C. Hogg. Extending the Point Distribution Model using polar coordinates. Image & Vision Computing, 14(8):589--599, August 1995.

....by considering whether any model facets lie in front of it. ffl Use a non linear modelling technique to improve the accuracy and specificity of the hand model, thus improving tracking. We have already developed one extension to the PDM which allows for a better modelling of pivotal motion [16]. Initial experiments using this model for 3D tracking are inconclusive at present; there may be inherent instability problems. ffl Improve the model s mesh configuration in some way. At present, the distribution of vertices over the model surface is roughly uniform. However, it is apparent that ....

A.J. Heap and D.C. Hogg. Extending the Point Distribution Model using polar coordinates. In Proc. CAIP, Prague, Czech Republic, September 1995. Also available as ftp://agora.leeds.ac.uk/scs/doc/reports/ 1995/95 25.ps.Z.

....problem. The Polynomial Regression PDM [7] allows landmark points to move along combinations of polynomial paths; however the computational complexity required is high, and structures experiencing large amounts of pivotal or bending motion still cause problems. The Cartesian Polar Hybrid PDM [8] helps to overcome these limitations. By selectively reparameterizing landmark points into polar coordinates, bending and pivotal deformation can be linearized and thus modelled more accurately. For maximum flexibility, polar mapped points are allowed to pivot about any other model point, with ....

....as either Cartesian or polar, and polar points must have a pivot and axis reference chosen. This can be done by hand but ideally it should be automated. We previously used a classification algorithm which found mappings by maximizing the model s compactness , measured quantitatively) see [8] for details) This worked well, but assumed that all the necessary pivot points had been marked on the training examples, which is not always the case. In this paper we propose a new classification method which discovers any pivotal deformation present via statistical analysis of the training ....

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A.J. Heap and D.C. Hogg. Extending the Point Distribution Model using polar coordinates. In Proc. CAIP, Prague, Czech Republic, September 1995.

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T. Heap and D. Hogg. Extending the point distribution model using polar coordinates. Image and Vision Computing, 14(8):589--599, 1996.

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