In this paper, we describe a novel focusing mechanism that uses a varifocal mirror and its application to measuring the shape of solder bumps arrayed on an LSI package board based on the shape-from-focus technique. We used a copper-alloy mirror deformed by a piezoelectric actuator as a varifocal mirror to build a simple yet fast focusing mechanism. The varifocal mirror was situated at the focal point of the image-taking lens in image space so that the lateral magnification was constant during focusing and an orthographic projection was perfectly established. The focused plane could be shifted along the optical axis with a precision of 1.4 µm in a depth range of 1.3 mm by driving the varifocal mirror. A magnification of 1.97 was maintained during focusing. Evaluating the curvature of field and removing its effect from the depth data reduced errors. The shapes of 208 solder bumps, 260 µm high and arrayed at a pitch of 500 µm on the board, were measured. The entire 10 mm10 mm board was segmented into 34 partly overlapping sections. We captured 101 images in each section with a high-resolution camera at different focal points at 15 µm intervals. The shape of almost the entire upper hemisphere of a solder bump could be measured. The error in measuring the bump heights was less than 12 µm.

This paper proposes a precise method of realizing simultaneous measurement of microscopic defects and the macroscopic three-dimensional shapes of planar objects having specular reflection surfaces. The direction vector field of surface tilt is evaluated directly by the introduction of a moving slit-light technique based on computer graphic animation. A reflected image created by the moving slit-light is captured by a video camera, and the image sequence of the slit-light deformation is analyzed. The obtained direction vector field of the surface tilt recovers the surface shape by means of integration. Two sample objects, a concave mirror and a plane plastic injection molding, are tested to measure the performance of the proposed method. Surface anomalies such as surface dent and warpage are detected quantitatively at a high resolution (about 0.2 [µm]) and a high accuracy (about 95%) in a wide area (about 15 [cm]) of the test object.

The conventional shape from focus (SFF) methods have inaccuracies because of piecewise constant approximation of the focused image surface (FIS). We propose a more accurate scheme for SFF based on representation of three-dimensional FIS in terms of neural network weights. The neural networks are trained to learn the shape of the FIS that maximizes the focus measure.

Texture has been investigated as a cue for reconstructing 3-D structure. There are various textures in a natural scene. In this paper, the regularity of alignment of texture elements was manipulated to investigate its effect on human perception. The results show that the regularity affects human perception when only the texel density gradient is given as cue or the density cue is inconsistent with the compression cue. We introduce a model based on a MAP estimation to account for the result from a viewpoint of an integration of 3-D cues. The model simultaneously estimates texture properties and 3-D surface orientation by using prior knowledge about texture and 3-D surface. The performance of the model accounts for the experimental result well.

High-speed display of 3-D objects in virtual reality environments is one of the currently important subjects. Shape simplification is considered an efficient method. This paper presents a method of hierarchical cube-based segmentation for shape simplification and multiresolution model construction. The relations among shape simplification, resolution and visual distance are derived firstly. The first level model is generated from scattered range data by cube-base segmentation with the first level cube size. Multiresolution models are then generated by re-sampling polygonal patch vertices of each former level model with hierarchical cube-based segmentation structure. The results show that the algorithm is efficient for constructing multiresolution models of free-form shape 3-D objects from scattered range data and high compression ratio can be obtained with little noticeable difference during the visualization.

In this paper we propose a new application of Wu's mechanical theorem proving method to reconstruct polyhedra in 3-D space from their projection image. First we set up three groups of equations. The first group is of the geometric relations expressing that vertices are on a plane segment, on a line segment, and forming angle in 3-D space. The second is of those relations on image plane. And the rest is of the relations between the vertices in 3-D space and their correspondence on image plane. Next, we classify all the groups of equations into two sets, a set of hypotheses and a conjecture. We apply this method to seven cases of models. Then, we apply Wu's method to prove that the hypotheses follow the conjecture and obtain pseudodivided remainders of the conjectures, which represent relations of angles or lengths between 3-D space and their projected image. By this method we obtained new geometrical relations for seven cases of models. We also show that, in the region in image plane where corresponding spatial measures cannot reconstructed, leading coefficients of hypotheses polynomials approach to zero. If the vertex of an image angle is in such regions, we cannot calculate its spatial angle by direct manipulation of the hypothesis polynomials and the conjecture polynomial. But we show that by stability analysis of the pseudodivided remainder the spatial angles can be calculated even in those regions.