The Alignment of Objects With Smooth Surfaces: Error Analysis of the Curvature Method

The recognition of objects with smooth bounding surfaces from their contour images is considerably more complicated than that of objects with sharp edges, since in the former case the set of object points that generates the silhouette contours changes from one view to another. The "curvature method", developed by Basri and Ullman [1988], provides a method to approximate the appearance of such objects from different viewpoints. In this paper we analyze the curvature method. We apply the method to ellipsoidal objects and compute analytically the error obtained for different rotations of the objects. The error depends on the exact shape of the ellipsoid (namely, the relative lengths of its axes), and it increases a sthe ellipsoid becomes "deep" (elongated in the Z-direction). We show that the errors are usually small, and that, in general, a small number of models is required to predict the appearance of an ellipsoid from all possible views. Finally, we show experimentally that the curvature method applies as well to objects with hyperbolic surface patches.

Object Recognition By Alignment Using Invariant Projections of Planar Surfaces

In order to recognize an object in an image, we must determine the best transformation from object model to the image. In this paper, we show that for features from coplanar surfaces which undergo linear transformations in space, there exist projections invariant to the surface motions up to rotations in the image field. To use this property, we propose a new alignment approach to object recognition based on centroid alignment of corresponding feature groups. This method uses only a single pair of 2D model and data. Experimental results show the robustness of the proposed method against perturbations of feature positions.

The Perception of Subjective Surfaces

It is proposed that subjective contours are an artifact of the perception of natural three-dimensional surfaces. A recent theory of surface interpolation implies that "subjective surfaces" are constructed in the visual system by interpolation between three-dimensional values arising from interpretation of a variety of surface cues. We show that subjective surfaces can take any form, including singly and doubly curved surfaces, as well as the commonly discussed fronto-parallel planes. In addition, it is necessary in the context of computational vision to make explicit the discontinuities, both in depth and in surface orientation, in the surfaces constructed by interpolation. It is proposed that subjective surfaces and subjective contours are demonstrated. The role played by figure completion and enhanced brightness contrast in the determination of subjective surfaces is discussed. All considerations of surface perception apply equally to subjective surfaces.

Core-Shell Assisted Bimetallic Assembly of Pt and Ru Nanoparticles by DNA Hybridization

We have discovered that the current protocols to assemble Au nanoparticles based on DNA hybridization do not work well with the small metal nanoparticles (e.g. 5 nm Au, 3.6 nm Pt and 3.2 nm Ru particles). Further investigations revealed the presence of strong interaction between the oligonucleotide backbone and the surface of the small metal nanoparticles. The oligonucleotides in this case are recumbent on the particle surface and are therefore not optimally oriented for hybridization. The nonspecific adsorption of oligonucleotides on small metal nanoparticles must be overcome before DNA hybridization can be accepted as a general assembly method. Two methods have been suggested as possible solutions to this problem. One is based on the use of stabilizer molecules which compete with the oligonucleotides for adsorption on the metal nanoparticle surface. Unfortunately, the reported success of this approach in small Au nanoparticles (using K₂BSPP) and Au films (using 6-mercapto-1-hexanol) could not be extended to the assembly of Pt and Ru nanoparticles by DNA hybridization. The second approach is to simply use larger metal particles. Indeed most reports on the DNA hybridization induced assembly of Au nanoparticles have made use of relatively large particles (>10 nm), hinting at a weaker non-specific interaction between the oligonucleotides and large Au nanoparticles. However, most current methods of nanoparticle synthesis are optimized to produce metal nanoparticles only within a narrow size range. We find that core-shell nanoparticles formed by the seeded growth method may be used to artificially enlarge the size of the metal particles to reduce the nonspecific binding of oligonucleotides. We demonstrate herein a core-shell assisted growth method to assemble Pt and Ru nanoparticles by DNA hybridization. This method involves firstly synthesizing approximately 16 nm core-shell Ag-Pt and 21 nm core-shell Au-Ru nanoparticles from 9.6 nm Ag seeds and 17.2 nm Au seeds respectively by the seed-mediated growth method. The core-shell nanoparticles were then functionalized by complementary thiolated oligonucleotides followed by aging in 0.2 M PBS buffer for 6 hours. The DNA hybridization induced bimetallic assembly of Pt and Ru nanoparticles could then be carried out in 0.3 M PBS buffer for 10 hours.