# Fabric Defect Detection Using L0 Gradient Minimization and Fuzzy C-Means
## 2 Related Works  
Plain and twill fabric detection methods can be classified into five aspects: Spectral [9; 10], learning [11; 12], statistical [13; 14; 15], model-based [16; 17], and structural methods [18; 19]. The spectral method based on the Wavelet transform [20] achieved 97.5% detection accuracy with five known defect types and a 93.3% detection accuracy (a slight drop) with three unknown defect types in an evaluation. The statistical method applied gray relational analysis with co-occurrence Matrix (CM) features [21] on Jacquard fabric images, reaching 94% detection accuracy for 50 defective samples. The learning method via three-layer back-propagation neural network and thresholding of the image analysis [22] was tested on the same kind of fabric; it achieved 94.38% accuracy, using 240 samples of the four defect classes. The limitation of their method includes a longer training time, because of the larger number of inner layers and the danger of over-training. In addition, model-based approach using the Gaussian mixture model [23] was successfully applied to Brodatz mosaic image segmentation and fabric defect detection. Structural approaches based on normalized cross-correlation algorithm [24] obtained a higher detection success rate of 95% on twelve defective plain and twill fabrics' images. In general, many pieces of research on plain and twill fabric inspection works have achieved fruitful results; however, these methods were not efficiently evaluated on complicated patterned fabrics and statistical-texture fabrics.  
The defect detection of complicated patterned fabric has been increasing during the last decade. The Bollinger bands (BB) and regular bands (RB) [25] methods employed the regularity property in the patterned texture to carry out defect detection on dot-, box- and star-patterned fabrics. They also obtained accuracy rates of 98.59% (167 defect-free and 171 defective images) and 99.4% (80 defect-free and 86 defective images), respectively. The wavelet-preprocessing golden image subtraction (WGIS) method [20] achieved 96.7% accuracy on 30 defect-free and 30 defective patterned images by using a golden image to perform moving subtraction of each pixel along each row of every wavelet-pre-processed tested image. The ID [8] method obtained the detection accuracies range from 94.9-99.6% for dot- (110 defect-free and 120 defective samples), star- (25 defect-free and 25 defective samples) and box-patterned fabrics (30 defect-free and 26 defective samples), which decomposed a fabric image into structures of cartoon (defective objects) and texture (repeated patterns). A recent Elo rating method [26] achieved an overall 97.07% detection success rate based on databases of [8]. However, it remains unknown whether the patterned fabric defect detection method can also be applied to twill, plain fabric, and statistical-texture fabrics.  
In our work, we take full consideration of the original fabric images, which can be seen as defective structure information and texture information. Texture information often affects the fabric defect detection. LGM is used to filter the images to remove the texture information. In this way, the filtered fabric images would quickly locate and segment the defects. The proposed method can detect the defect in the plain fabric, twill fabric, star-patterned fabric, dot-patterned fabric, box-patterned fabric, striped fabric, and statistical-texture fabric.