Robust defect detection for near-regular textures based on Hermann Weyl’s discrepancy measure

G. Stübl. Robust defect detection for near-regular textures based on Hermann Weyl’s discrepancy measure. 1, 2014.

  • Gernot Stübl

Finding similarities or dissimilarities between images or parts of them is a vital task in many image processing applications, e.g. stereo vision, tracking or template matching. Often researchers use traditional measures like sum of squared differences or normalized cross-correlation without reflecting on whether there is a better choice for their applications. However, especially for translational transformations, these traditional measures are proven to generate local minima/maxima as unwanted artifacts. Hermann Weyl’s discrepancy norm, on the other hand, is a special dissimilarity measure with outstanding properties such as monotonic increase of dissimilarity with increasing displacement, and frequency independence through a Lipschitz boundedness. These properties induce a direct link between a dissimilarity value and the amount of displacement. Goals of this thesis are 1) to illustrate and explore the properties of the discrepancy norm, 2) to find image processing areas where the properties of the discrepancy norm are useful, 3) to demonstrate these benefits on real world problems/data.

As an introduction, various experimental setups demonstrate properties of the discrepancy norm, for example, the well behaved cost functions even under disturbances such as heavy Gaussian noise. Based on experimental analysis, we chose two domains where the application of discrepancy norm is beneficial: periodicity estimation and visual defect detection for textiles.

For the former, discrepancy norm can be used as a robust displacement function for space domain periodicity estimation, leading to estimation accuracies in the range of the state of the art on standardized datasets. The advantage over current state of the art is that, without changing parameters, discrepancy norm can be used for both regular and near-regular textures.

In the field of visual defect detection, template matching is formulated as a general optimization problem. We present three approaches to solve this problem. The first one builds on a Lipschitzian global optimization, while the second one utilizes a random-based search strategy. The benefit of the second approach is that it is nearly parameter-free. A third approach, that is also nearly parameter-free, utilizes approximate nearest neighbor fields (ANNFs) that originate from structural image editing. To demonstrate the practicability of the proposed approaches, we tested them on a standardized dataset and compared them to state-of-the-art algorithms. The results for defect detection in a combination with a linear Support Vector Machine classifier are in the range of the state of the art with the benefit of nearly parameter-free configuration and motivate further research on this topic.