Fig. 1. Images from the DocuCenter: (a) A part of the MRZ correctly captured. (b) The MRZ with cropped last characters. (c) Several letters are made defective by the hologram reflection.

Fig. 2. (a) A new object defined between two inflection points. (b) Affine coordinates system. (c) If such a curve is a part of our contour, this method of approximation is unusable.

Fig. 3. (a) The basic parallelogram. (b) One step of the cutting algorithm. (c) The approximation after the second phase.

Fig. 5. (a and b) The second and third phase of the contour approximation in the affine coordinates. (c) The original image in original coordinates.

Fig. 4. (o₁–o₁t₂): The first object and its affine transformation, (o₂–o₂t₂), (o₃–o₃t₂), (o₄–o₄t₂): The second, third, fourth objects and their affine transformation, respectively.

Fig. 6. Examples of two objects, on which inflection points were detected.

Fig. 7. (co_i) are the original complex objects, (cot_j) are the transformed and partially occluded complex objects.

Fig. 8. (o₁) corresponds to (ot₁) where the teapot was transformed with d = 0.4 and 50% of the contour was occluded, (o₂) corresponds to (ot₂) where the snake was transformed with d = 0.5 and 50% of the contour was occluded, (o₃) corresponds to (ot₃) where the plane was transformed with d = 0.4 and 40% of the contour was occluded, (o₄) corresponds to (ot₄) where the teapot was transformed with d = 0.2 and 40% of the contour was occluded.

Fig. 9. Samples of the images with additive noise.

Fig. 10. I₁, I₂ labels in every image the original points of inflection. We computed the penalty function between the image with original inflection points and the images, where the inflection points were chosen from the highlighted interval. The size of the interval is 10% of the length of original border.

Fig. 11. This graph corresponds to Fig. 10 and shows the penalty function between the original object and the object which had its inflection points shifted. The x axis represents (in a %) how much the first and the second inflection points were shifted together. The y axis is the penalty function. Diamonds represent o₁, x-marks o₂, triangles o₃ and squares o₄.

Fig. 12. (a1)–(d1) Several examples of tested objects. (a2)–(d2) Examples of several segmented objects.

Fig. 13. (a1) The original image of the stopper. (b1) The image of the stopper under strong projective transformation. (a2) Original image of the pliers. (b2) The pliers contour change is caused by the pliers non-zero depth and relatively big angle of the camera inclination. The white curves on image a2, b2 highlight the places where the contours were most changed.

Penalty function of the original object and the object transformed by affine transformation

The penalty function is not zero due to discretisation problem by affine transformation when strong skewing presented.

The penalty function of all original objects

The correspondence (as a percentage) between the original and transformed and occluded objects

The recognition results

For the object skewed with d = 0.1 and with 20% of the contour occluded, the probability of correct recognition is 93.8%(from our four template objects).

In the remaining cases the recognition process delivers false results – the percentage of matched border is higher for another template – or the similarity score for all object is zero.

The recognition success of the Lamdans method

The mean of the penalty function between the original images and 100 realizations of additive noise to images with given σ²

The numbers in the brackets represent the real width and height of the original images.

Please compare the penalty function from the graph to the penalty function between different shreds (Table 2).

You can see, that the penalty function between all tested different shreds is greater than between shreds and noisy shreds although σ² was up to 64.

This shows very good stability to additive noise.