Optical Splitting Trees for High-Precision Monocular Imaging

In this article, we consider the design of monocular multiview optical systems that form optical splitting trees, where the optical path topology takes the shape of a tree because of recursive beam splitting. Designing optical splitting trees is challenging when it requires many views with specific spectral properties. We introduce a manual design paradigm for optical splitting trees and a computer-assisted design tool to create efficient splitting-tree cameras. The tool accepts as input a specification for each view and a set of weights describing the user's relative affinity for efficiency, measurement accuracy, and economy. An optimizer then searches for a design that maximizes these weighted priorities. Our tool's output is a splitting-tree design that implements the input specification and an analysis of the efficiency of each root-to-leaf path. Automatically designed trees appear comparable to those designed by hand; we even show some cases where they are superior. With the help of the optimizer, the system demonstrates high dynamic range, focusing, matting, and hybrid imaging implemented on a single, reconfigurable camera containing eight sensors     

Rational Filters for Passive Depth from Defocus

A fundamental problem in depth from defocus is the measurement of relative defocus between images. The performance of previously proposed focus operators are inevitably sensitive to the frequency spectra of local scene textures. As a result, focus operators such as the Laplacian of Gaussian result in poor depth estimates. An alternative is to use large filter banks that densely sample the frequency space. Though this approach can result in better depth accuracy, it sacrifices the computational efficiency that depth from defocus offers over stereo and structure from motion. We propose a class of broadband operators that, when used together, provide invariance to scene texture and produce accurate and dense depth maps. Since the operators are broadband, a small number of them are sufficient for depth estimation of scenes with complex textural properties. In addition, a depth confidence measure is derived that can be computed from the outputs of the operators. This confidence measure permits further refinement of computed depth maps. Experiments are conducted on both synthetic and real scenes to evaluate the performance of the proposed operators. The depth detection gain error is less than 1%, irrespective of texture frequency. Depth accuracy is found to be 0.51.2% of the distance of the object from the imaging optics.     

Effects of Weathering on Treatment of Lead Contaminated Soils

Treatment of lead-contaminated material focuses on the reduction of leached lead concentrations in laboratory leaching tests. There has been little study on the chemical stability of treated materials after waste disposal. To investigate the effects of weathering on several solidification/stabilization chemistries, lead-contaminated soil was treated with various agents (cement, phosphates, dithiocarbamate, calcium hydroxide, calcium carbonate, and metallic iron) and subjected to natural weathering for one year. Lead concentrations and pH values in field percolates and leachates from toxicity characteristic leaching procedure (TCLP) and water leaching tests were used to evaluate changes in the treatment effectiveness. Weathering altered the treatment chemistry of several additives—alkaline additives were neutralized, while reduced additives were oxidized. Lead concentrations in field percolates from the untreated soil were around 1.0?mg/L, and did not vary over one year of weathering time. After one year of weathering, lead concentrations in field percolates from most samples were reduced to low levels (<0.15 mg/L). Weathering also affected lead concentrations in the TCLP and water leach test leachates from the treated wastes. Treated wastes in which the alkaline additives were neutralized or reduced additives oxidized gave higher TCLP lead concentrations after weathering than before, in contrast to the decreasing lead concentrations in the field percolates. Water leaching tests on the alkaline treated wastes had lower lead concentrations after weathering than before.     

Parametric Feature Detection

Most visual features are parametric in nature, including, edges, lines, corners, and junctions. We propose an algorithm to automatically construct detectors for arbitrary parametric features. To maximize robustness we use realistic multi-parameter feature models and incorporate optical and sensing effects. Each feature is represented as a densely sampled parametric manifold in a low dimensional subspace of a Hilbert space. During detection, the vector of intensity values in a window about each pixel in the image is projected into the subspace. If the projection lies sufficiently close to the feature manifold, the feature is detected and the location of the closest manifold point yields the feature parameters. The concepts of parameter reduction by normalization, dimension reduction, pattern rejection, and heuristic search are all employed to achieve the required efficiency. Detectors have been constructed for five features, namely, step edge (five parameters), roof edge (five parameters), line (six parameters), corner (five parameters), and circular disc (six parameters). The results of detailed experiments are presented which demonstrate the robustness of feature detection and the accuracy of parameter estimation.     

Stereo and Specular Reflection

The problem of accurate depth estimation using stereo in the presence of specular reflection is addressed. Specular reflection, a fundamental and ubiquitous reflection mechanism, is viewpoint dependent and can cause large intensity differences at corresponding points, resulting in significant depth errors. We analyze the physics of specular reflection and the geometry of stereopsis which lead to a relationship between stereo vergence, surface roughness, and the likelihood of a correct match. Given a lower bound on surface roughness, an optimal binocular stereo configuration can be determined which maximizes precision in depth estimation despite specular reflection. However, surface roughness is difficult to estimate in unstructured environments. Therefore, trinocular configurations, independent of surface roughness are determined such that at each scene point visible to all sensors, at least one stereo pair can produce correct depth. We have developed a simple algorithm to reconstruct depth from the multiple stereo pairs.     

Corneal Imaging System: Environment from Eyes

This paper provides a comprehensive analysis of exactly what visual information about the world is embedded within a single image of an eye. It turns out that the cornea of an eye and a camera viewing the eye form a catadioptric imaging system. We refer to this as a corneal imaging system. Unlike a typical catadioptric system, a corneal one is flexible in that the reflector (cornea) is not rigidly attached to the camera. Using a geometric model of the cornea based on anatomical studies, its 3D location and orientation can be estimated from a single image of the eye. Once this is done, a wide-angle view of the environment of the person can be obtained from the image. In addition, we can compute the projection of the environment onto the retina with its center aligned with the gaze direction. This foveated retinal image reveals what the person is looking at. We present a detailed analysis of the characteristics of the corneal imaging system including field of view, resolution and locus of viewpoints. When both eyes of a person are captured in an image, we have a stereo corneal imaging system. We analyze the epipolar geometry of this stereo system and show how it can be used to compute 3D structure. The framework we present in this paper for interpreting eye images is passive and non-invasive. It has direct implications for several fields including visual recognition, human-machine interfaces, computer graphics and human affect studies. This research was conducted while the first author was affiliated with Columbia University. A shorter version of this paper appeared in (Nishino and Nayar, 2004).     

Quasiperiodic (QP) oscillations in electrical power systems

The occurrence of quasiperiodic (QP) oscillations in power systems, a phenomena hitherto unknown, was first experienced in the French grid when attempting to energize an unloaded transformer at the end of a long transmission line. There are no simple analytical tools available to study conditions for the occurrence of QP oscillations. In this paper, the conditions necessary for the occurrence of quasiperiodicity are shown by solving the system equations using the method of harmonic balance. It is shown that QP oscillations will occur due to the severity of magnetizing nonlinearity of the transformer core. It is also shown that if core losses are high, only frequency locked oscillations can occur. The results are confirmed by numerical solution on the original set of differential equations.     

Reflectance based object recognition

Neighboring points on a smoothly curved surface have similar surface normals and illumination conditions. Therefore, their brightness values can be used to compute the ratio of their reflectance coefficients. Based on this observation, we develop an algorithm that estimates a reflectance ratio for each region in an image with respect to its background. The algorithm is efficient as it computes ratios for all image regions in just two raster scans. The region reflectance ratio represents a physical property that is invariant to illumination and imaging parameters. Several experiments are conducted to demonstrate the accuracy and robustness of ratio invariant.The ratio invariant is used to recognize objects from a single brightness image of a scene. Object models are automatically acquired and represented using a hash table. Recognition and pose estimation algorithms are presented that use ratio estimates of scene regions as well as their geometric properties to index the hash table. The result is a hypothesis for the existence of an object in the image. This hypothesis is verified using the ratios and locations of other regions in the scene. This approach to recognition is effective for objects with printed characters and pictures. Recognition experiments are conducted on images with illumination variations, occlusions, and shadows. The paper is concluded with a discussion on the simultaneous use of reflectance and geometry for visual perception.     

A simple algorithm for nearest neighbor search in high dimensions

The problem of finding the closest point in high-dimensional spaces is common in pattern recognition. Unfortunately, the complexity of most existing search algorithms, such as k-d tree and R-tree, grows exponentially with dimension, making them impractical for dimensionality above 15. In nearly all applications, the closest point is of interest only if it lies within a user-specified distance ϵ. We present a simple and practical algorithm to efficiently search for the nearest neighbor within Euclidean distance ϵ. The use of projection search combined with a novel data structure dramatically improves performance in high dimensions. A complexity analysis is presented which helps to automatically determine ϵ in structured problems. A comprehensive set of benchmarks clearly shows the superiority of the proposed algorithm for a variety of structured and unstructured search problems. Object recognition is demonstrated as an example application. The simplicity of the algorithm makes it possible to construct an inexpensive hardware search engine which can be 100 times faster than its software equivalent. A C++ implementation of our algorithm is available