Shape evaluation of highly overlapped powder grains using U-Net-based deep learning segmentation network

Abstract

With the advancement of electron microscopy, industrial microscale objects are analyzed through image-based characterization. However, the automated and objective assessment of a vast number of images required for quality control is limited by the incomplete segmentation of individual objects in the image. In this study, the scanning electron microscope images of powder grains are selected as target images representing industrial microscale objects. A deep neural network based on the U-Net is developed and trained by manually labeled ground truth. Although the U-Net is a basic network originally devised for biomaterials, the network in this study achieves approximately 90% accuracy and outperforms conventional thresholding methods. However, the boundaries distinguishing individual are not completely classified. The inference results are further processed with morphological operations and watershed algorithms to quantitatively measure grain shapes. Discrepancies in shape parameters between ground truth and network prediction are also discussed.

Graphic Abstract

Appendix

This section briefly explains the shape indices discussed in this study. A more detailed explanation of these descriptors and additional indices are found in the work of Olson (Olson 2011).

The AR of an object is defined as the ratio of the maximum Feret diameter (F_max) to the minimum Feret diameter (F_min). The Feret diameter is the size of an object along a specified orientation. The longest distance between any two parallel tangent lines of the object boundary is F_max; conversely, the shortest distance between any two parallel tangent lines on the object is F_min.

The circularity (C) of an object represents the similarity of the object to a circle and is calculated as follows:

$$C=\sqrt{4\pi A/{P}^{2}},$$

(A1)

where A and P are the area and perimeter of the particle, respectively.

The convex hull of an object can be explained as the shape of the elastic and tense bounding string of an object. The perimeter (P_C) and area (A_C) of the convex hull are distinguished from those of the original object by subscript C.

The convexity (H_P) of an object is defined as the ratio of P_C to P. The maximum value of H_P is unity and is achieved when the shape of the object is the same as that of the convex hull. From unity, H_P decreases as the shape deviates from the convex hull and becomes more complex. The solidity (H_A) of an object is an area-based measure of the extent that the shape of the object deviates from its convex hull; H_A is defined as A divided by A_C.