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

Objective Distinctions Between Genuine Plane Symmetries and Pseudosymmetries in Crystal Patterns of Graphic Artwork

A recently developed method for the objective identification of the plane symmetry group of a noisy crystal pattern is briefly described and subsequently applied to two pieces of graphic art. Pseudo-symmetries do not distract from the beauty of graphic art but add to it. They are here distinguished from the genuine symmetries that combine to form the best-fitting plane symmetry group. The gray-value deviations of the individual pixel values of graphic artworks from their perfectly symmetric abstractions are considered to be chiefly due to the handiwork and employed creative procedures of an individual artists. As different graphic techniques/procedures were employed in the creation of the here classified crystal patterns, one may glean insights on how well a particular technique or procedure supports the realization of an intended crystallographic symmetry group in a graphic work of art.Comment: 8 pages, 3 figure

Optimality of Maximum Likelihood Estimation for GeometricFitting and the KCR Lower Bound

Geometric fitting is one of the most fundamental problems of computer vision. In [8], the author derived a theoretical accuracy bound (KCR lower bound) for geometric fitting in general and proved that maximum likelihood (ML) estimation is statistically optimal. Recently, Chernov and Lesort [3] proved a similar result, using a weaker assumption. In this paper, we compare their formulation with the author’s and describe the background of the problem. We also review recent topics including semiparametric models and discuss remaining issues

Further improving geometric fitting

We give a formal definition of geometric fitting in a way that suits computer vision applications. We point out that the performance of geometric fitting should be evaluated in the limit of small noise rather than in the limit of a large number of data as recommended in the statistical literature. Taking the KCR lower bound as an optimality requirement and focusing on the linearized constraint case, we compare the accuracy of Kanatani's renormalization with maximum likelihood (ML) approaches including the FNS of Chojnacki et al. and the HEIV of Leedan and Meer. Our analysis reveals the existence of a method superior to all these. </p

DAC: Detector-Agnostic Spatial Covariances for Deep Local Features

Current deep visual local feature detectors do not model the spatial uncertainty of detected features, producing suboptimal results in downstream applications. In this work, we propose two post-hoc covariance estimates that can be plugged into any pretrained deep feature detector: a simple, isotropic covariance estimate that uses the predicted score at a given pixel location, and a full covariance estimate via the local structure tensor of the learned score maps. Both methods are easy to implement and can be applied to any deep feature detector. We show that these covariances are directly related to errors in feature matching, leading to improvements in downstream tasks, including solving the perspective-n-point problem and motion-only bundle adjustment. Code is available at https://github.com/javrtg/DA

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

this paper investigates the meaning of &quot;statistical methods&quot; for geometric inference based on image feature points. We point out that statistical analysis does not make sense unless the underlying &quot;statistical ensemble&quot; 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 &quot;geometric fitting&quot;, &quot;geometric model selection&quot;, the &quot;geometric AIC&quot;, and the &quot;geometric MDL&quot;. Referring to such statistical concepts as &quot;nuisance parameters &quot;, the &quot;Neyman-Scott problem&quot;, and &quot;semiparametric models&quot;, we point out that simulation experiments for performance evaluation will lose meaning without carefully considering the assumptions involved and intended application

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

Towards Generalized Noise-Level Dependent Crystallographic Symmetry Classifications of More or Less Periodic Crystal Patterns

Geometric Akaike Information Criteria (G-AICs) for generalized noise-level dependent crystallographic symmetry classifications of two-dimensional (2D) images that are more or less periodic in either two or one dimensions as well as Akaike weights for multi-model inferences and predictions are reviewed. Such novel classifications do not refer to a single crystallographic symmetry class exclusively in a qualitative and definitive way. Instead, they are quantitative, spread over a range of crystallographic symmetry classes, and provide opportunities for inferences from all classes (within the range) simultaneously. The novel classifications are based on information theory and depend only on information that has been extracted from the images themselves by means of maximal likelihood approaches so that these classifications are objective. This is in stark contrast to the common practice whereby arbitrarily set thresholds or null hypothesis tests are employed to force crystallographic symmetry classifications into apparently definitive/exclusive states, while the geometric feature extraction results on which they depend are never definitive in the presence of generalized noise, i.e., in all real-world applications. Thus, there is unnecessary subjectivity in the currently practiced ways of making crystallographic symmetry classifications, which can be overcome by the approach outlined in this review