IMPROVING RANSAC FEATURE MATCHING BASED ON GEOMETRIC RELATION

Feature Matching between images is an essential task for many computer vision and photogrammetry applications, such as Structure from Motion (SFM), Surface Extraction, Visual Simultaneous Localization and Mapping (VSLAM), and vision-based localization and navigation. Among the matched point pairs, there are typically false positive matches. Therefore, outlier detection and rejection are important steps in any vision application. RANSAC has been a well-established approach for outlier detection. The outlier ratio and the number of required correspondences used in RANSAC determine the number of iterations needed, which ultimately, determines the computation time. We propose a simple algorithm (GR_RANSAC) based on the two-dimensional spatial relationships between points in the image domain. The assumption is that the distances and bearing angles between the 2D feature points should be similar in images with small disparity, such as the case for video image sequences. In the proposed approach, the distances and angles are measured from a reference point in the first image and its correspondence in the other image, and the points with any significant differences are considered as outliers. This process can pre-filter the matched points, and thus increase the inliers’ ratio. As a result, GR_RANSAC can converge to the correct hypothesis in fewer trial runs than ordinary RANSAC.

From mythology to science: the development of scientific hydrological concepts in Greek antiquity and its relevance to modern hydrology

Whilst hydrology is a Greek term, it was not in use in the Classical literature, but much later, during the Renaissance, in its Latin form, hydrologia. On the other hand, Greek natural philosophers (or, in modern vocabulary, scientists) created robust knowledge in related scientific areas, to which they gave names such as meteorology, climate and hydraulics. These terms are now in common use internationally. Greek natural philosophers laid the foundation for hydrological concepts and the hydrological cycle in its entirety. Knowledge development was brought about by searches for technological solutions to practical problems as well as by scientific curiosity. While initial explanations belong to the sphere of mythology, the rise of philosophy was accompanied by the quest for scientific descriptions of the phenomena. It appears that the first geophysical problem formulated in scientific terms was the explanation of the flood regime of the Nile, then regarded as a paradox because of the spectacular difference from the river flow regime in Greece, i.e. the fact that the Nile flooding occurs in summer when in most of the Mediterranean the rainfall is very low. While the early attempts were unsuccessful, Aristotle was able to formulate a correct hypothesis, which he tested through what appears to be the first scientific expedition in history, in the transition from the Classical to Hellenistic periods. The Hellenistic period brought advances in all scientific fields including hydrology, an example of which is the definition and measurement of flow discharge by Heron of Alexandria. These confirm the fact that the hydrological cycle was well understood in Ancient Greece, yet it poses the question why correct explanations were not accepted and, instead, why ancient and modern mythical views were preferred up to the 18th century.

Top program construction and reduction for polynomial time Meta-Interpretive learning

Meta-Interpretive Learners, like most ILP systems, learn by searching for a correct hypothesis in the hypothesis space, the powerset of all constructible clauses. We show how this exponentially-growing search can be replaced by the construction of a Top program: the set of clauses in all correct hypotheses that is itself a correct hypothesis. We give an algorithm for Top program construction and show that it constructs a correct Top program in polynomial time and from a finite number of examples. We implement our algorithm in Prolog as the basis of a new MIL system, Louise, that constructs a Top program and then reduces it by removing redundant clauses. We compare Louise to the state-of-the-art search-based MIL system Metagol in experiments on grid world navigation, graph connectedness and grammar learning datasets and find that Louise improves on Metagol’s predictive accuracy when the hypothesis space and the target theory are both large, or when the hypothesis space does not include a correct hypothesis because of “classification noise” in the form of mislabelled examples. When the hypothesis space or the target theory are small, Louise and Metagol perform equally well.

From mythology to science: the development of scientific hydrological concepts in the Greek antiquity and its relevance to modern hydrology

Whilst hydrology is a Greek term, it has not been in use in the Classical literature but much later, during the Renaissance, in its Latin version, hydrologia. On the other hand, Greek natural philosophers created robust knowledge in related scientific areas, to which they gave names such as meteorology, climate and hydraulics. These terms are now in common use internationally. Within these areas, Greek natural philosophers laid the foundation of hydrological concepts and the hydrological cycle in its entirety. Knowledge development was brought about by search for technological solutions to practical problems, as well as by scientific curiosity to explain natural phenomena. While initial explanations belong to the sphere of mythology, the rise of philosophy was accompanied by attempts to provide scientific descriptions of the phenomena. It appears that the first geophysical problem formulated in scientific terms was the explanation of the flood regime of the Nile, then regarded as a paradox because of the spectacular difference from the river flow regime in Greece and other Mediterranean regions, i.e., the fact that the Nile flooding occurs in summer when in most of the Mediterranean the rainfall is very low. While some of the early attempts to explain it were influenced by Homer’s mythical view (archaic period), eventually, Aristotle was able to formulate a correct hypothesis, which he tested through what it appears to be the first in history scientific expedition, in the turn from the Classical to Hellenistic period. This confirms the fact that the hydrological cycle was well understood during the Classical period yet it poses the question why Aristotle’s correct explanation had not been accepted and, instead, ancient and modern mythical views had been preferred up to the 18th century.

Explanation Supports Hypothesis Generation in Learning

A large body of research has shown that engaging in explanation improves learning across a range of tasks. The act of explaining has been proposed to draw attention and cognitive resources toward evidence that will support a good explanation—information that is broad, abstract, and consistent with prior knowledge—which in turn aids discovery and generalization. However, it remains unclear whether explanation acts on the learning process via improved hypothesis generation, increasing the probability that the correct hypothesis is considered in the first place, or hypothesis evaluation, the appraisal of the correct hypothesis in light of evidence. In the present study, we address this question by separating the hypothesis generation and evaluation processes in a novel category learning task and quantifying the effect of explanation on each process independently. We find that explanation supports the generation of broad and abstract hypotheses but has less effect on the evaluation of hypotheses.

Beyond generalization: Enhancing accurate interpretation of flexible models

ABSTRACTMachine learning optimizes flexible models to predict data. In scientific applications, there is a rising interest in interpreting these flexible models to derive hypotheses from data. However, it is unknown whether good data prediction guarantees accurate interpretation of flexible models. We test this connection using a flexible, yet intrinsically interpretable framework for modeling neural dynamics. We find that many models discovered during optimization predict data equally well, yet they fail to match the correct hypothesis. We develop an alternative approach that identifies models with correct interpretation by comparing model features across data samples to separate true features from noise. Our results reveal that good predictions cannot substitute for accurate interpretation of flexible models and offer a principled approach to identify models with correct interpretation.

Hypothesis Testing on Regression: Investigating Students’ Skill

This study aims to investigate students’ ability to write a correct hypothesis based on the statement referring to regression coefficients. Different statements of regression coefficients, specifically the slope were given in the standard format of test questions and the students were asked to conduct an appropriate hypothesis test. From the decision made, the students also had to provide suitable conclusions on each of the tests conducted. 197 answer scripts were inspected and the focus was given to the hypothesis statement and the conclusion provided by the students. The results indicated that students were able to write proper hypothesis statement for a regression coefficient that directly refers to the slope of the variable. However, they failed to provide correct hypothesis when they had to translate the definition of slope to an appropriate hypothesis statement. Despite their ability to write simple hypothesis for regression slope, they still had difficulties in providing conclusions for the tests conducted. The study also clearly revealed that even though some of the students managed to write proper conclusions, they did not correspond to the hypothesis statements given earlier, as the conclusions made were merely based on the question statement.

A prior-based approach for hypothesis comparison and its utility to discern among temporal scenarios of divergence

One of the major problems in evolutionary biology is to elucidate the relationships between historical events and the tempo and mode of lineage divergence. The development of relaxed molecular clock models and the increasing availability of DNA sequences resulted in more accurate estimations of taxa divergence times. However, finding the link between competing historical events and divergence is still challenging. Here we investigate assigning constrained-age priors to nodes of interest in a time-calibrated phylogeny as a means of hypothesis comparison. These priors are equivalent to historic scenarios for lineage origin. The hypothesis that best explains the data can be selected by comparing the likelihood values of the competing hypotheses, modelled with different priors. A simulation approach was taken to evaluate the performance of the prior-based method and to compare it with an unconstrained approach. We explored the effect of DNA sequence length and the temporal placement and span of competing hypotheses (i.e. historic scenarios) on selection of the correct hypothesis and the strength of the inference. Competing hypotheses were compared applying a posterior simulation analogue of the Akaike Information Criterion and Bayes factors (obtained after calculation of the marginal likelihood with three estimators: Harmonic Mean, Stepping Stone and Path Sampling). We illustrate the potential application of the prior-based method on an empirical data set to compare competing geological hypotheses explaining the biogeographic patterns in Pleurodeles newts. The correct hypothesis was selected on average 89% times. The best performance was observed with DNA sequence length of 3500-10000 bp. The prior-based method is most reliable when the hypotheses compared are not temporally too close. The strongest inferences were obtained when using the Stepping Stone and Path Sampling estimators. The prior-based approach proved effective in discriminating between competing hypotheses when used on empirical data. The unconstrained analyses performed well but it probably requires additional computational effort. Researchers applying this approach should rely only on inferences with moderate to strong support. The prior-based approach could be applied on biogeographical and phylogeographical studies where robust methods for historical inferences are still lacking.

Conditional modeling and the jitter method of spike resampling

The existence and role of fine-temporal structure in the spiking activity of central neurons is the subject of an enduring debate among physiologists. To a large extent, the problem is a statistical one: what inferences can be drawn from neurons monitored in the absence of full control over their presynaptic environments? In principle, properly crafted resampling methods can still produce statistically correct hypothesis tests. We focus on the approach to resampling known as jitter. We review a wide range of jitter techniques, illustrated by both simulation experiments and selected analyses of spike data from motor cortical neurons. We rely on an intuitive and rigorous statistical framework known as conditional modeling to reveal otherwise hidden assumptions and to support precise conclusions. Among other applications, we review statistical tests for exploring any proposed limit on the rate of change of spiking probabilities, exact tests for the significance of repeated fine-temporal patterns of spikes, and the construction of acceptance bands for testing any purported relationship between sensory or motor variables and synchrony or other fine-temporal events.

How Undergraduate Students Misread Cladograms

Although phylogenetic systematics is used to reconstruct evolutionar 123y relationships, undergraduates have a difficult time mastering its fundamental concepts. Because it is a key part of the mainstream professional thinking, we explored in what ways students misread cladograms, which are the abstract and synthetic diagrams of phylogenetic systematics. We developed a questionnaire to examine the following four hypotheses as to how introductory college-level students (n=51) read cladograms: 1) students read cladograms correctly; 2) students infer that proximity of tips equals relatedness; 3) students read cladograms as they might an evolutionary tree, reading left to right as primitive to more advanced, and perceiving organisms as branching off; and 4) students infer ancestors at the nodes. Most responses fell into one of the four hypotheses, with 55% following the scientific (‘correct’) hypothesis. Most students answered between six and eight of the ten questions correctly. Slightly more than half of the students generally followed the scientific hypothesis, while others applied both the scientific and proximity (hypothesis 2, above) hypotheses together. A few students followed the primitive hypothesis (hypothesis 3, above). Our recommendation is that instructors address discrepancies between the scientific and proximity hypotheses in particular. For undergraduates, generally, cladograms require focused teaching, explanation, and active-learning approaches to be successfully used to teach phylogenetic systematics.