This can alternatively be formulated by examining the changes of intensity due to shifts in a local window. Around a corner point, the image intensity will change greatly when the window is shifted in an arbitrary direction. Following this intuition and through a clever decomposition, the Harris detector uses the second moment matrix as the basis of its corner decisions. (See corner detection for more complete derivation). The matrix formula_1, has also been called the autocorrelation matrix and has values closely related to the derivatives of image intensity.  where formula_3 and formula_4 are the respective derivatives (of pixel intensity) in the formula_5 and formula_6 direction at point (formula_7,formula_8); formula_7 and formula_8 are the position parameters of the weighting function w. The off-diagonal entries are the product of formula_3 and formula_4, while the diagonal entries are squares of the respective derivatives. The weighting function formula_13 can be uniform, but is more typically an isotropic, circular Gaussian,  that acts to average in a local region while weighting those values near the center more heavily. As it turns out, this formula_1 matrix describes the shape of the autocorrelation measure as due to shifts in window location. Thus, if we let formula_16 and formula_17 be the eigenvalues of formula_1, then these values will provide a quantitative description of how the autocorrelation measure changes in space: its principal curvatures. As Harris and Stephens (1988) point out, the formula_1 matrix centered on corner points will have two large, positive eigenvalues. Rather than extracting these eigenvalues using methods like singular value decomposition, the Harris measure based on the trace and determinant is used:  where formula_21 is a constant. Corner points have large, positive eigenvalues and would thus have a large Harris measure. Thus, corner points are identified as local maxima of the Harris measure that are above a specified threshold.  where formula_23 are the set of all corner points, formula_24 is the Harris measure calculated at formula_5, formula_26 is an 8-neighbor set centered on formula_27 and formula_28 is a specified threshold. A Gaussian scale space representation of an image is the set of images that result from convolving a Gaussian kernel of various sizes with the original image. In general, the representation can be formulated as:  where formula_30 is an isotropic, circular Gaussian kernel as defined above.