arXiv subjects

Todd Zickler

Publications and source records attributed to Todd Zickler.

29 records · Page 2Linked to original sources

arXiv2021

Level Set Binocular Stereo with Occlusions

Localizing stereo boundaries and predicting nearby disparities are difficult because stereo boundaries induce occluded regions where matching cues are absent. Most modern computer vision algorithms treat occlusions secondarily (e.g., via left-right consistency checks after matching) or rely on high-level cues to improve nearby disparities (e.g., via deep networks and large training sets). They ignore the geometry of stereo occlusions, which dictates that the spatial extent of occlusion must equal the amplitude of the disparity jump that causes it. This paper introduces an energy and level-set optimizer that improves boundaries by encoding occlusion geometry. Our model applies to two-layer, figure-ground scenes, and it can be implemented cooperatively using messages that pass predominantly between parents and children in an undecimated hierarchy of multi-scale image patches. In a small collection of figure-ground scenes curated from Middlebury and Falling Things stereo datasets, our model provides more accurate boundaries than previous occlusion-handling stereo techniques. This suggests new directions for creating cooperative stereo systems that incorporate occlusion cues in a human-like manner.

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arXiv2021

Level Set Stereo for Cooperative Grouping with Occlusion

Localizing stereo boundaries is difficult because matching cues are absent in the occluded regions that are adjacent to them. We introduce an energy and level-set optimizer that improves boundaries by encoding the essential geometry of occlusions: The spatial extent of an occlusion must equal the amplitude of the disparity jump that causes it. In a collection of figure-ground scenes from Middlebury and Falling Things stereo datasets, the model provides more accurate boundaries than previous occlusion-handling techniques.

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arXiv2021

Determining Generic Point Configurations From Unlabeled Path or Loop Lengths

Let $\mathbf{p}$ be a configuration of $n$ points in $\mathbb{R}^d$ for some $n$ and some $d \ge 2$. Each pair of points defines an edge, which has a Euclidean length in the configuration. A path is an ordered sequence of the points, and a loop is a path that has the same endpoints. A path or loop, as a sequence of edges, also has a Euclidean length. In this paper, we study the question of when $\mathbf{p}$ will be uniquely determined (up to an unknowable Euclidean transform) from a given set of path or loop lengths. In particular, we consider the setting where the lengths are given simply as a set of real numbers, and are not labeled with the combinatorial data describing the paths or loops that gave rise to the lengths. Our main result is a condition on the set of paths or loops that is sufficient to guarantee such a unique determination. We also provide an algorithm, under a real computational model, for performing a reconstruction of $\mathbf{p}$ from such unlabeled lengths. To obtain our results, we introduce a new family of algebraic varieties which we call the unsquared measurement varieties. The family is parameterized by the number of points $n$ and the dimension $d$, and our results follow from a complete characterization of the linear automorphisms of these varieties for all $n$ and $d$. The linear automorphisms for the special case of $n = 4$ and $d = 2$ correspond to the so-called Regge symmetries of the tetrahedron.

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arXiv2020

Linear Symmetries of the Unsquared Measurement Variety

We introduce a new family of algebraic varieties, $L_{d,n}$, which we call the unsquared measurement varieties. This family is parameterized by a number of points $n$ and a dimension $d$. These varieties arise naturally from problems in rigidity theory and distance geometry. In those applications, it can be useful to understand the group of linear automorphisms of $L_{d,n}$. Notably, a result of Regge implies that $L_{2,4}$ has an unexpected linear automorphism. In this paper, we give a complete characterization of the linear automorphisms of $L_{d,n}$ for all $n$ and $d$. We show, that apart from $L_{2,4}$ the unsquared measurement varieties have no unexpected automorphisms. Moreover, for $L_{2,4}$ we characterize the full automorphism group.

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arXiv2018

Tackling 3D ToF Artifacts Through Learning and the FLAT Dataset

Scene motion, multiple reflections, and sensor noise introduce artifacts in the depth reconstruction performed by time-of-flight cameras. We propose a two-stage, deep-learning approach to address all of these sources of artifacts simultaneously. We also introduce FLAT, a synthetic dataset of 2000 ToF measurements that capture all of these nonidealities, and allows to simulate different camera hardware. Using the Kinect 2 camera as a baseline, we show improved reconstruction errors over state-of-the-art methods, on both simulated and real data.

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arXiv2016

Understanding Symmetric Smoothing Filters: A Gaussian Mixture Model Perspective

Many patch-based image denoising algorithms can be formulated as applying a smoothing filter to the noisy image. Expressed as matrices, the smoothing filters must be row normalized so that each row sums to unity. Surprisingly, if we apply a column normalization before the row normalization, the performance of the smoothing filter can often be significantly improved. Prior works showed that such performance gain is related to the Sinkhorn-Knopp balancing algorithm, an iterative procedure that symmetrizes a row-stochastic matrix to a doubly-stochastic matrix. However, a complete understanding of the performance gain phenomenon is still lacking. In this paper, we study the performance gain phenomenon from a statistical learning perspective. We show that Sinkhorn-Knopp is equivalent to an Expectation-Maximization (EM) algorithm of learning a Gaussian mixture model of the image patches. By establishing the correspondence between the steps of Sinkhorn-Knopp and the EM algorithm, we provide a geometrical interpretation of the symmetrization process. This observation allows us to develop a new denoising algorithm called Gaussian mixture model symmetric smoothing filter (GSF). GSF is an extension of the Sinkhorn-Knopp and is a generalization of the original smoothing filters. Despite its simple formulation, GSF outperforms many existing smoothing filters and has a similar performance compared to several state-of-the-art denoising algorithms.

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arXiv2015

Low-level Vision by Consensus in a Spatial Hierarchy of Regions

We introduce a multi-scale framework for low-level vision, where the goal is estimating physical scene values from image data---such as depth from stereo image pairs. The framework uses a dense, overlapping set of image regions at multiple scales and a "local model," such as a slanted-plane model for stereo disparity, that is expected to be valid piecewise across the visual field. Estimation is cast as optimization over a dichotomous mixture of variables, simultaneously determining which regions are inliers with respect to the local model (binary variables) and the correct co-ordinates in the local model space for each inlying region (continuous variables). When the regions are organized into a multi-scale hierarchy, optimization can occur in an efficient and parallel architecture, where distributed computational units iteratively perform calculations and share information through sparse connections between parents and children. The framework performs well on a standard benchmark for binocular stereo, and it produces a distributional scene representation that is appropriate for combining with higher-level reasoning and other low-level cues.

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arXiv2014

Monte Carlo non local means: Random sampling for large-scale image filtering

We propose a randomized version of the non-local means (NLM) algorithm for large-scale image filtering. The new algorithm, called Monte Carlo non-local means (MCNLM), speeds up the classical NLM by computing a small subset of image patch distances, which are randomly selected according to a designed sampling pattern. We make two contributions. First, we analyze the performance of the MCNLM algorithm and show that, for large images or large external image databases, the random outcomes of MCNLM are tightly concentrated around the deterministic full NLM result. In particular, our error probability bounds show that, at any given sampling ratio, the probability for MCNLM to have a large deviation from the original NLM solution decays exponentially as the size of the image or database grows. Second, we derive explicit formulas for optimal sampling patterns that minimize the error probability bound by exploiting partial knowledge of the pairwise similarity weights. Numerical experiments show that MCNLM is competitive with other state-of-the-art fast NLM algorithms for single-image denoising. When applied to denoising images using an external database containing ten billion patches, MCNLM returns a randomized solution that is within 0.2 dB of the full NLM solution while reducing the runtime by three orders of magnitude.

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arXiv2014

Modeling Radiometric Uncertainty for Vision with Tone-mapped Color Images

To produce images that are suitable for display, tone-mapping is widely used in digital cameras to map linear color measurements into narrow gamuts with limited dynamic range. This introduces non-linear distortion that must be undone, through a radiometric calibration process, before computer vision systems can analyze such photographs radiometrically. This paper considers the inherent uncertainty of undoing the effects of tone-mapping. We observe that this uncertainty varies substantially across color space, making some pixels more reliable than others. We introduce a model for this uncertainty and a method for fitting it to a given camera or imaging pipeline. Once fit, the model provides for each pixel in a tone-mapped digital photograph a probability distribution over linear scene colors that could have induced it. We demonstrate how these distributions can be useful for visual inference by incorporating them into estimation algorithms for a representative set of vision tasks.

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arXiv2014

From Shading to Local Shape

We develop a framework for extracting a concise representation of the shape information available from diffuse shading in a small image patch. This produces a mid-level scene descriptor, comprised of local shape distributions that are inferred separately at every image patch across multiple scales. The framework is based on a quadratic representation of local shape that, in the absence of noise, has guarantees on recovering accurate local shape and lighting. And when noise is present, the inferred local shape distributions provide useful shape information without over-committing to any particular image explanation. These local shape distributions naturally encode the fact that some smooth diffuse regions are more informative than others, and they enable efficient and robust reconstruction of object-scale shape. Experimental results show that this approach to surface reconstruction compares well against the state-of-art on both synthetic images and captured photographs.

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arXiv2012

Image Restoration with Signal-dependent Camera Noise

This article describes a fast iterative algorithm for image denoising and deconvolution with signal-dependent observation noise. We use an optimization strategy based on variable splitting that adapts traditional Gaussian noise-based restoration algorithms to account for the observed image being corrupted by mixed Poisson-Gaussian noise and quantization errors.

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