PhD Student, Center for Applied Math, Cornell University

Advisors: Noah Snavely and Kavita Bala

Committee: David Bindel and Bob Connelly

Office: 345 Gates Hall

Email: klw229 at cornell.edu

Academic CV

Dissertation: Robustly Modeling the World from Photos (10 MB PDF)

I am no longer on the job market! I've accepted a position teaching Computer Science and Math at Washington College starting in fall 2016.

I'm a fifth-year graduate student working on a class of 3D reconstruction problems in computer vision called Structure from Motion (SfM). In my work we recover 3D models, such as in the images below, from hundreds to tens of thousands of tourist photos of famous world landmarks. Point cloud renderings of Sacre Coeur Cathedral and Piccadilly Circus are below. Essentially these are geometric inverse problems, where we try to recover 3D Euclidean geometry based on images under a set of unknown pinhole projections.

Since consumer cameras have many optical distortions, and because correctly matching up points in one image with corresponding points in another is quite difficult, SfM problems are typically noisy optimizations. Patterns in point-to-image visibility give an underlying graph structure, so problems can have an interesting mixture of discrete and continuous topologies.

TA: MATH 2940, Linear Algebra for Engineers, Fall 2011

TA: CS 4670: Intro to Computer Vision, Fall 2012

TA: MATH 1920: Calculus III for Engineers, Fall 2013

TA: CS 4820: Intro to Analysis of Algorithms, Summer 2015

TA: CURIE Academy (camp for STEM-interested high school girls)

Instructional TA: MATH 1110 Calculus I, Fall 2015

Fundamental Matrix slides—a stand alone lecture on the fundamental matrix and the eight point algorithm in two-view stereo (12MB PDF).

Recent SfM research has especially focused on ways to formulate 3D reconstruction as a single large optimization, rather than incrementally growing a seed model.

In this paper, we give a simple reformulation of a step of this larger optimization, as well as a novel way to filter for outlier measurements. We call this outlier detection 1DSfM, because we show how projecting problem instances onto a single dimension reveals 1D ordering problems which are easier to solve.

The most difficult scenes for SfM usually contain repeated structures. For example, the four sides of the Big Ben clock tower all look nearly indistinguishable up close, so algorithms often compute constraints amounting to "the north side of the building is the south side". The resulting reconstructions are broken, perhaps with extra ghosted copies of towers and domes, but even sometimes with a complete failure to reconstruct.

In this paper we leverage the redundancy of data in our large models. We locate mistakes by finding signature structures in a visibility graph. We remove these mistakes to build a correct 3D model.

From images alone, a 3D reconstruction can only be computed up to a similarity. Without extra information, the scale, location, and orientation of the model are undetermined. GPS tags can help some, but they are noisy and many images lack them.

In this paper we accurately georegister 3D reconstructions with the help of images from Google Street View and 3D models from Google Earth. We show that these complememtary data sources allow interesting applications, such as computing depth maps, or accurately classifying scene normals.