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A parameterised contour that is invariant against affine transformations is a convenient substitution of the object image for shape recognition. Generally, parameterisation needs several representative signals of the image contour to fit the affine transformation model. When the representative signals fail to carry the contour information thoroughly, information loss occurs in the resulting parameterised contour, and so the accuracy of shape recognition may deteriorate. Synthesised feature signals are shown, which represent that an image contour without information loss can be extracted with partial Fourier synthesis or partial cosine synthesis. Lossless parameterisation of the image contour is obtained by substituting the synthesised feature signals into the affine invariant function. Experimental results verify its representative, affine invariance and recognition rate in shape recognition. The results are compared with those by partial wavelet synthesis, which has insignificant information loss.