Prasanna Rangarajan

Hyper least squares fitting of circles and ellipses

This work extends the circle fitting method of Rangarajan and Kanatani (2009) to accommodate ellipse fitting. Our method, which we call HyperLS, relies on algebraic distance minimization with a carefully chosen scale normalization. The normalization is derived using a rigorous error analysis of least squares (LS) estimators so that statistical bias is eliminated up to second order noise terms. Numerical evidence suggests that the proposed HyperLS estimator is far superior to the standard LS and is slightly better than the Taubin estimator. Although suboptimal in comparison to maximum likelihood (ML), our HyperLS does not require iterations. Hence, it does not suffer from convergence issues due to poor initialization, which is inherent in ML estimators. In this sense, the proposed HyperLS is a perfect candidate for initializing the ML iterations.

HyperLS for Parameter Estimation in Geometric Fitting

We present a general framework of a special type of least squares (LS) estimator, which we call “HyperLS, ” for parameter estimation that frequently arises in computer vision applications. It minimizes the algebraic distance under a special scale normalization, which is derived by a detailed error analysis in such a way that statistical bias is removed up to second order noise terms. We discuss in detail many theoretical issues involved in its derivation. By numerical experiments, we show that HyperLS is far superior to the standard LS and comparable in accuracy to maximum likelihood (ML), which is known to produce highly accurate results but may fail to converge if poorly initialized. We conclude that HyperLS is a perfect candidate for ML initialization.

Active computational imaging for circumventing resolution limits at macroscopic scales

Macroscopic imagers are subject to constraints imposed by the wave nature of light and the geometry of image formation. The former limits the resolving power while the latter results in a loss of absolute size and shape information. The suite of methods outlined in this work enables macroscopic imagers the unique ability to capture unresolved spatial detail while recovering topographic information. The common thread connecting these methods is the notion of imaging under patterned illumination. The notion is advanced further to develop computational imagers with resolving power that is decoupled from the constraints imposed by the collection optics and the image sensor. These imagers additionally feature support for multiscale reconstruction.

Structured Light Optical Super-Resolution: Encoding for Limited Optical Bandwidth

Structured illumination finds widespread use in microscopy and optical profilometry. A marriage of the principle underlying these methods promises novel solutions to the resolution problem that plagues consumer cameras.

Estimating homographies without normalization

Existing linear methods for estimating homographies, rely on coordinate normalization, to reduce the error in the estimated homography. Unfortunately, the estimated homography depends on the choice of the normalization. The proposed extension to the (linear) Taubin estimator is the perfect substitute for such methods, as it does not rely on coordinate normalization, and produces homographies whose error is consistent with existing methods. Also, unlike existing linear methods, the proposed Taubin estimator is theoretically unbiased, and unaffected by similarity transformations of the correspondences in the two views. In addition, it can be adapted to estimate other quantities such as trifocal tensors.

Pushing the limits of digital imaging using structured illumination

The present work describes an active stereo apparatus that can not only recover scene geometry but also resolve spatial detail beyond the camera optical cutoff. The apparatus is comprised of a camera and a projector whose center-of-perspective is located in the camera pupil plane1. The scene is illuminated with warped sinusoidal patterns as opposed to periodic or coded patterns. The findings reported in this work can help design imaging systems that feature improved optical resolution and 3D acquisition capabilities.

Geometric model for an independently tilted lens and sensor with application for omnifocus imaging

Optical imaging systems in which the lens and sensor are free to rotate about independent pivots offer greater degrees of freedom for controlling and optimizing the process of image gathering. However, to benefit from the expanded possibilities, we need an imaging model that directly incorporates the essential parameters. In this work, we propose a model of imaging which can accurately predict the geometric properties of the image in such systems. Furthermore, we introduce a new method for synthesizing an omnifocus (all-in-focus) image from a sequence of images captured while rotating a lens. The crux of our approach lies in insights gained from the new model.

Space-Variant Optical Super-Resolution using Sinusoidal Illumination

The present work extends the scope of Optical Super-Resolution to imaging systems with spatially-varying blur, by using sinusoidal illumination. It also establishes that knowledge of the space-variant blur is not a pre-requisite for super-resolution.

Active illumination computational imaging for optical super resolution, 3D topography, and indirect imaging

Structured illumination has been utilized to super-resolve microscopic objects and provide topographic information in computer vision applications. Motivated by the achievements in these fields and leveraging techniques found in astronomical sparse aperture systems, an approach is developed to super-resolve macroscopic objects in typical real world scenarios. The challenges of super-resolving uncontrolled 3D environments are addressed. An approach is presented which enables the collection of 3D topographic information while super-resolving. These techniques use incoherent illumination to resolve spatial detail in an intensity image. For indirect imaging scenarios, this approach is adapted with structured coherent illumination to super-resolve phase at a distance.

Challenges for the future of imaging: what's next and where can we draw inspiration from? (Conference Presentation)

Recent advances in computation, optical projection, and non-traditional imaging sensor designs are making it possible to overcome classical optical challenges which have stood for centuries: breaking resolution “limits” in real world scenarios and capturing indirect images of obscured objects.