For Geometric Inference from Images, What Kind of Statistical Model Is Necessary?

In order to facilitate smooth communications with researchers in other fields including statistics, this paper investigates the meaning of "statistical methods" for geometric inference based on image feature points, We point out that statistical analysis does not make sense unless the underlying "statistical ensemble" is clearly defined. We trace back the origin of feature uncertainty to image processing operations for computer vision in general and discuss the implications of asymptotic analysis for performance evaluation in reference to "geometric fitting", "geometric model selection", the "geometric AIC", and the "geometric MDL". Referring to such statistical concepts as "nuisance parameters", the "Neyman-Scott problem", and "semiparametric models", we point out that simulation experiments for performance evaluation will lose meaning without carefully considering the assumptions involved and intended applications

Model Selection for Geometric Fitting: Geometric Ale and Geometric MDL

Contrasting "geometric fitting", for which the noise level is taken as the asymptotic variable, with "statistical inference", for which the number of observations is taken as the asymptotic variable, we give a new definition of the "geometric AIC" and the "geometric MDL" as the counterparts of Akaike's AIC and Rissanen's MDL. We discuss various theoretical and practical problems that emerge from our analysis. Finally, we show, doing experiments using synthetic and real images, that the geometric MDL does not necessarily outperform the geometric AIC and that the two criteria have very different characteristics

Automatic Camera Model Selection for Multibody Motion Segmentation

We study the problem of segmenting independently moving objects in a video sequence. Several algorithms exist for classifying the trajectories of the feature points into independent motions, but the performance depends on the validity of the underlying camera imaging model. In this paper, we present a scheme for automatically selecting the best model using the geometric AIC before the segmentation stage, Using real video sequences, we confirm that the segmentation accuracy indeed improves if the segmentation is based on the selected model. We also show that the trajectory data can be compressed into low-dimensional vectors using the selected model. This is very effective in reducing the computation time for a long video sequence

Geometric BIC

The author introduced the "geometric AIC" and the "geometric MDL" as model selection criteria for geometric fitting problems. These correspond to Akaike’s "AIC" and Rissanen's "BIC", respectively, well known in the statistical estimation framework. Another criterion well known is Schwarz’ "BIC", but its counterpart for geometric fitting has been unknown. This paper introduces the corresponding criterion, which we call the "geometric BIC", and shows that it is of the same form as the geometric MDL. We present the underlying logical reasoning of Bayesian estimation

A PSF-based approach to Kepler/K2 data. I. Variability within the K2 Campaign 0 star clusters M 35 and NGC 2158

Kepler and K2 data analysis reported in the literature is mostly based on aperture photometry. Because of Kepler's large, undersampled pixels and the presence of nearby sources, aperture photometry is not always the ideal way to obtain high-precision photometry and, because of this, the data set has not been fully exploited so far. We present a new method that builds on our experience with undersampled HST images. The method involves a point-spread function (PSF) neighbour-subtraction and was specifically developed to exploit the huge potential offered by the K2 "super-stamps" covering the core of dense star clusters. Our test-bed targets were the NGC 2158 and M 35 regions observed during the K2 Campaign 0. We present our PSF modeling and demonstrate that, by using a high-angular-resolution input star list from the Asiago Schmidt telescope as the basis for PSF neighbour subtraction, we are able to reach magnitudes as faint as Kp~24 with a photometric precision of 10% over 6.5 hours, even in the densest regions. At the bright end, our photometric precision reaches ~30 parts-per-million. Our method leads to a considerable level of improvement at the faint magnitudes (Kp>15.5) with respect to the classical aperture photometry. This improvement is more significant in crowded regions. We also extracted raw light curves of ~60,000 stars and detrended them for systematic effects induced by spacecraft motion and other artifacts that harms K2 photometric precision. We present a list of 2133 variables.Comment: 27 pages (included appendix), 2 tables, 25 figures (5 in low resolution). Accepted for publication in MNRAS on November 05, 2015. Online materials will be available on the Journal website soo

Incorporating Human Beliefs and Behaviors into Wildlife Ecology

Like much of the global biosphere, wildlife species have experienced rapid declines during the Anthropocene. Wildlife ecologists have responded to these crises by developing a range of technologies, techniques, and large datasets, which together have revolutionized the field, provided novel insights into the movements and behaviors of animals, and identified new risks and impacts to wildlife in a human-dominated world. While these advances have been vitally important, wildlife ecology has been slower to recognize and incorporate humans themselves into its new research domains. The chapters of this dissertation explore methods for better incorporating human behaviors, beliefs, actions, and infrastructure into the theories and approaches in wildlife ecology that have flourished in the last two decades. The research presented here demonstrates the importance of linking human beliefs and behaviors to wildlife ecology both by presenting novel findings and by showing the opportunities missed when narrow approaches are applied to complex socio-ecological problems.In Chapter 1, I provide a general introduction on the theories underlying this research, contextualize the research questions in light of the loss and recovery of large predators, and describe the research site where I collected much of the data for this dissertation. In Chapter 2, I apply the methods of movement ecology to some of the first fine-scale telemetry data collected on rifle hunters. I draw conclusions about their individual, site-level, and regional-level hunting behaviors and discuss the broad implications of these findings for hunting management. In Chapter 3, I examine livestock-predator conflict using approaches from both ecology and the social sciences. I describe a form of selection bias that is likely widespread but unreported due to the omission of social data from ecological models of conflict, and I offer guidelines for combining and translating ecological and social research on conflict. In Chapter 4, I explore the ecological impacts of one of the most globally widespread human constructions, the fence. I show for the first time the potential extent of fencing at large scales and discuss the wide variety of ecological effects of fences for both humans and ecosystems. I further highlight biases and gaps in fence research that have thus far limited a complete understanding of the environmental effects of these features. In Chapter 5, I conclude by making recommendations regarding how research might better incorporate human perceptions, decisions, and actions into ecology

Universal Geometric Camera Calibration with Statistical Model Selection

We propose a new universal camera calibration approach that uses statistical information criteria for automatic camera model selection. It requires the camera to observe a planar pattern from different positions, and then closed-form estimates for the intrinsic and extrinsic parameters are computed followed by nonlinear optimization. In lieu of modeling radial distortion, the lens projection of the camera is modeled, and in addition we include decentering distortion. This approach is particularly advantageous for wide angle (fisheye) camera calibration because it often reduces the complexity of the model compared to modeling radial distortion. We then apply statistical information criteria to automatically select the complexity of the camera model for any lens type. The complete algorithm is evaluated on synthetic and real data for several different lens projections, and a comparison between existing methods which use radial distortion is done

Improved Multistage Learning for Multibody Motion Segmentation

We present an improved version of the MSL method of Sugaya and Kanatani for multibody motion segmentation. We replace their initial segmentation based on heuristic clustering by an analytical computation based on GPCA, fitting two 2-D affine spaces in 3-D by the Taubin method. This initial segmentation alone can segment most of the motions in natural scenes fairly correctly, and the result is successively optimized by the EM algorithm in 3-D, 5-D, and 7-D. Using simulated and real videos, we demonstrate that our method outperforms the previous MSL and other existing methods. We also illustrate its mechanism by our visualization technique