Therefore, for each pixel in the image we use the following observation window: where c is the current pixel. We then calculate the following products: Finally the algorithm checks whether up > down and down > 127. The main disadvantage of this algorithm is low contrast images where too many pixels are eliminated from the original image. Therefore, the Hough transform cannot correctly estimate the tilt angle. 1.3 The Hough transform The Hough transform is an algorithm invented by Paul Hough in 1962. It was designed to detect particular features of common shapes such as circles or lines in digitized images. The classical transform is limited to features that can be described in parametric form. Therefore, the generalized Hough transform was introduced for features with more complex analytical form. In this section we will only describe the classical Hough transform for straight line detection. 1.3.1 Hough space In a two-dimensional space, a line can be represented through the two parameters x and y: and can be plotted for any pair (x, y) of image points. The main idea of ​​the Hough transform for straight line detection is to consider each line with its slope parameter a and its intercept parameter b, instead of x and y coordinates. However, this representation has some weaknesses, especially when we have to represent a vertical line. In this case the slope parameter approaches infinity. Therefore, for computational reasons, it is simpler to represent a line with the common parameters ρ and θ, where ρ is the distance from the line to the origin and θ the angle of the line. Thereafter, using this parameterization the line equation can be rewritten as follows: An infinite histogram... center of the paper... is taken as the estimated tilt angle. 1.6.2 Alignment using grayscale images This algorithm uses only grayscale image information to estimate the tilt angle. It is based on the grayscale image filtering algorithm 1.2.2, the Sobel edge detection filter and the classical Hough transform. The input image is first filtered using the grayscale image filter. For each pixel that meets the filter conditions, the Sobel edge detection algorithm is applied and the gradient directory φ is calculated using equation (1.4). An estimate of the tilt angle at the current point is: Therefore, instead of voting in all directions, voting can be performed for only a few values ​​of θ. To maintain accuracy, votes are performed between θ − 2◦ and θ + 2◦. The peaks in the accumulator are identified using the method proposed in 1.5.2.