Gibbs Random Field Model Based Weight Selection for the 2-D Adaptive Weighted Median Filter

establish electrical connections between components on multilayered circuit boards. Conditions such as excess filling and lack of filling cause electrical defects. The sample shown in Fig. 9 has a cavity, indicating lack of filling. The specular reflectance and variable size of the tungsten particles gives the surface a random texture. In this case, a total of 18 images were taken using stage position increments of 8 gm. Some of these images are shown in Fig. 9(a)-(f). Fig. 9(g) and Fig. 9(h) show a reconstructed image and two views of the depth map, respectively. The image reconstruction algorithm simply uses the estimated depth to locate and patch together the best focused image areas in image sequence. The depths maps have been filtered using a 5 x 5 median filter to remove a few scattered erroneous depths that result from the lack of texture in some image areas. The above experiments demonstrate the effectiveness of the shape from focus method. The results show that the Gaussian interpolation algorithm performs stably over a wide range of textures. No assumptions are made regarding the type of the textures. Small errors in computed depth estimates result from factors such as. image noise, Gaussian approximation of the SML focus measure function, and weak textures in some image areas. Some detail of the surface roughness is lost due to the use of a finite size window to compute focus measures. The above experiments were conducted on microscopic surfaces-that produce complex textured images. Such images are difficult, if not impossible, to analyze using recovery techniques such as shape from shading, photometric stereo, and structured light. These techniques work on surfaces with simple reflectance properties. Since the samples are microscopic in size, it is also difficult to use binocular stereo. Methods for recovering shape by texture analysis have been researched in the past. Typically, these methods recover shape information by analyzing the distortions in image texture due to surface orientation. The underlying assumption is that the surface texture has some regularity to it. Clearly, these approaches are not applicable to surfaces that produce random and spatially varying textures. For these reasons, shape from focus may be viewed as an effective method for objects with complex surface characteristics. ACKNOWLEDGMENT The authors would like to thank U. Shah for his help in implementing the automated system. This work has benefited from discussions with R. Willson of the VASC Group at CMU.