This paper presents a novel approach for the determination of depth as a function of blurring for automated visual inspection in VLSI wafer probing. There exists a smooth relationship between the degree of blur and the distance of a probe from a Test pad on a VLSI chip. Therefore, by measuring the amount of blurring, the distance from contact can be estimated. The effect of blurring on a point-object is studied in the frequency domain, and a monotonic relationship is found between the degree of blur and the frequency content of the image. Fourier feature extraction, with its inherent property of shift-invariance, is utilized to extract significant feature vectors. These vectors contain information on the degree of blur, and hence the distance from the probe. Neural networks are employed to map these feature vectors onto the actual distances. The network is then used in the recall mode to linearly interpolate the distance corresponding to the significant Fourier features of a blurred image.
I N T R O D U C T I O NComputer vision provides important sensory information in many robotic tasks. One of the most important tasks is the determination of depth, or the distance of an object in an image. This information is crucial for obstacle avoidance, navigation, poise determination, inspection, manipulation and assembly of objects etc. There are generally two methods employed, monocular and non-monocular. In monocular vision methods, the depth is obtained as a function of features present in the image, which is the case in this paper.
DEPTH FROM B L U R R I N GIn any photograph taken with a small depth of focus, there is a clue to the depth or distance of objects present. Those objects in focus are sharp and clear, while the ones in the background are blurred, so are the ones in the foreground. The further away from the focused plane an object is, the more blurred is its image.
2.1.Let 0 be an operation which maps a scene onto images. Given the input scene f, the result of applying 0 to f is denoted by 0 (f). Considering the operation 0 to be linear, i.e. 0 (af + bg) = a 0 ( f ) + b 0 (9) the image f can be considered to be a sum of point sources. Thus, knowledge of the operation's (0's) output for a point source input can be used to determine the output for f . The output of 0 for a point source input is called the Point Spread Function (PSF) of 0.
Measurement of Depth from Defocus -The Point Spread Function
The Mechanism of BlurringThe mechanism of blurring of the image of a point-object [I] is displayed in Fig.1 Points at a distance u > uo will be focused at a distance v behind the lens, but in front of the image plane as shown in fig.1. The blurred image of a point source, i.e., the PSF of the optical system thus corresponds to the degree of blur and can be used to estimate the distance of the point object. It can be approximated by a 2-D Gaussian G(r, U ) with a spatial constant U and radial distance r [l].
2.1.2.Pentland [l] further showed that depth D of the blurred point object is given by:
Dependence of Blur on ...
