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The ball grid array(BGA) chip is widely used in high density printed circuit board(PCB). However, inspection of defects in the solder joints is difficult by visual or a normal x-ray imaging method, because unlike conventional packages with guilwing type leads, solder joints of the BGA are located underneath its own package and ball type leads. Therefore, x-ray digital tomosynthesis(DT), which form a cross-sectional image of 3-D objects, is needed to image and inspect the solder joints of BGA. In this paper, we propose a series of algorithms for inspecting the solder joints of BGA by using x-ray crosssectional images that are acquired from the developed DT system. BGA solder joints are examined to check the alignment between the chip and pad on a PCB, bridge(electrically short), adequate solder volume. The volnme of the solder joint is represented by a gray level in the x-ray images : thus solderjoints can be examined by use ofthe gray-level profiles of each joint. To inspect and classify various defects, pattern classification method using a learning vector quantization(LVQ) neural network and a look up table(LUT) is proposed. The clusters into which a gray-level profile is classified are generated by the learning process ofthe network by using a number ofsampled gray-level profiles. A series ofthese developed algorithms for inspecting and classifying defects were tested on a number of BGA solder joints. The experimental results show that the proposed method yields satisfactory solutions for inspection based on x-ray cross-sectional images.

Histograms have been widely used for fast estimation of query result sizes in query optimization. In this paper, we propose a new histogram method, called the Skew-Tolerant Histogram (STHistogram) for two or three dimensional geographic data objects that are used in many real-world applications in practice.The proposed method provides a significantly enhanced accuracy in a robust manner even for the data set that has a highly skewed distribution. Our method detects hotspots present in various parts of a data set and exploits them in organizing histogram buckets. For this purpose, we first define the concept of a hotspot, and provide an algorithm that efficiently extracts hotspots from the given data set. Then, we present our histogram construction method that utilizes hotspot information. We also describe how to estimate query result sizes by using the proposed histogram. We show through extensive performance experiments that the proposed method provides better performance than other existing methods.