Читать книгу Rethinking Prototyping - Группа авторов - Страница 121

In the above formula (7), is the unit vector and λ is a factor ranging from zero to 255. Fig. 6 shows that the point cloud of the original image has one very clear axis of main extension. This axis corresponds approximately to ΔR/ΔG/ΔB. A method to determine the direction and magnitude of this vector precisely is the Eigenvalue decomposition. This procedure delivers what could be described as a data specific coordinate system. For an n-dimensional dataset, this consists of n linearly independent vectors (Eigenvector) and their corresponding scalars. Thereby, the first vector spans along the biggest variance in the input data. The following mutually perpendicular vectors have smaller and smaller scalars. Eigenvalue decomposition is used in principal component analysis (PCA), for example. Principal component because these are what matters most. Depending on the dataset, by only using the first few eigenvector or value pairs, it can be reconstructed with very high accuracy. In the present case, the colours C of the rebuilt image can be set to

P is the centre of gravity of the point cloud, is the first of the three eigenvectors, λ is again a scaling factor and d is the biggest diameter of the point cloud. Most wood texture images have a certain tonality equal over the entire image. A reconstruction applying this dimensionality reduction (projection of all the points on one line in space) still produces a very accurate result (Fig. 7, right) hardly distinguishable from the original.

Fig. 7 Original image (1st), reconstruction using two (2nd) and only the first (3rd) out of three eigenvectors

Because of its ease of implementation, the approach described first (Colour space) was chosen. Hereby the three-colour channels are preserved and can be treated separately for other calculations.