Edge detection is a projection

A desirable property of any edge detector is that it be a projection in the mathematical sense, that is, that when it is applied to its own output it produces no further change. This report examines the behaviour of some conventional and some new operators when applied to line-drawings. The Marr-Hildreth and some gradient operators are among the conventional operators examined. Also a class of energy feature detectors is explored. It is shown that the energy feature detector is a true projection and does not proliferate edges when applied to a line-drawing, whereas several of the conventional operators do.

Early spatial vision:a view through two eyes

Simple features such as edges are the building blocks of spatial vision, and so I ask: how arevisual features and their properties (location, blur and contrast) derived from the responses ofspatial filters in early vision; how are these elementary visual signals combined across the twoeyes; and when are they not combined? Our psychophysical evidence from blur-matchingexperiments strongly supports a model in which edges are found at the spatial peaks ofresponse of odd-symmetric receptive fields (gradient operators), and their blur B is givenby the spatial scale of the most active operator. This model can explain some surprisingaspects of blur perception: edges look sharper when they are low contrast, and when theirlength is made shorter. Our experiments on binocular fusion of blurred edges show that singlevision is maintained for disparities up to about 2.5*B, followed by diplopia or suppression ofone edge at larger disparities. Edges of opposite polarity never fuse. Fusion may be served bybinocular combination of monocular gradient operators, but that combination - involvingbinocular summation and interocular suppression - is not completely understood.In particular, linear summation (supported by psychophysical and physiological evidence)predicts that fused edges should look more blurred with increasing disparity (up to 2.5*B),but results surprisingly show that edge blur appears constant across all disparities, whetherfused or diplopic. Finally, when edges of very different blur are shown to the left and righteyes fusion may not occur, but perceived blur is not simply given by the sharper edge, nor bythe higher contrast. Instead, it is the ratio of contrast to blur that matters: the edge with theAbstracts 1237steeper gradient dominates perception. The early stages of binocular spatial vision speak thelanguage of luminance gradients.

Gradient-based reinforcement learning techniques for underwater robotics behavior learning

Darrerament, l'interès pel desenvolupament d'aplicacions amb robots submarins autònoms (AUV) ha crescut de forma considerable. Els AUVs són atractius gràcies al seu tamany i el fet que no necessiten un operador humà per pilotar-los. Tot i això, és impossible comparar, en termes d'eficiència i flexibilitat, l'habilitat d'un pilot humà amb les escasses capacitats operatives que ofereixen els AUVs actuals. L'utilització de AUVs per cobrir grans àrees implica resoldre problemes complexos, especialment si es desitja que el nostre robot reaccioni en temps real a canvis sobtats en les condicions de treball. Per aquestes raons, el desenvolupament de sistemes de control autònom amb l'objectiu de millorar aquestes capacitats ha esdevingut una prioritat. Aquesta tesi tracta sobre el problema de la presa de decisions utilizant AUVs. El treball presentat es centra en l'estudi, disseny i aplicació de comportaments per a AUVs utilitzant tècniques d'aprenentatge per reforç (RL). La contribució principal d'aquesta tesi consisteix en l'aplicació de diverses tècniques de RL per tal de millorar l'autonomia dels robots submarins, amb l'objectiu final de demostrar la viabilitat d'aquests algoritmes per aprendre tasques submarines autònomes en temps real. En RL, el robot intenta maximitzar un reforç escalar obtingut com a conseqüència de la seva interacció amb l'entorn. L'objectiu és trobar una política òptima que relaciona tots els estats possibles amb les accions a executar per a cada estat que maximitzen la suma de reforços totals. Així, aquesta tesi investiga principalment dues tipologies d'algoritmes basats en RL: mètodes basats en funcions de valor (VF) i mètodes basats en el gradient (PG). Els resultats experimentals finals mostren el robot submarí Ictineu en una tasca autònoma real de seguiment de cables submarins. Per portar-la a terme, s'ha dissenyat un algoritme anomenat mètode d'Actor i Crític (AC), fruit de la fusió de mètodes VF amb tècniques de PG.

Maximum principle, mean value operators and quasi boundedness in non-euclidean settings

This work deals with some classes of linear second order partial differential operators with non-negative characteristic form and underlying non- Euclidean structures. These structures are determined by families of locally Lipschitz-continuous vector fields in RN, generating metric spaces of Carnot- Carath´eodory type. The Carnot-Carath´eodory metric related to a family {Xj}j=1,...,m is the control distance obtained by minimizing the time needed to go from two points along piecewise trajectories of vector fields. We are mainly interested in the causes in which a Sobolev-type inequality holds with respect to the X-gradient, and/or the X-control distance is Doubling with respect to the Lebesgue measure in RN. This study is divided into three parts (each corresponding to a chapter), and the subject of each one is a class of operators that includes the class of the subsequent one. In the first chapter, after recalling “X-ellipticity” and related concepts introduced by Kogoj and Lanconelli in [KL00], we show a Maximum Principle for linear second order differential operators for which we only assume a Sobolev-type inequality together with a lower terms summability. Adding some crucial hypotheses on measure and on vector fields (Doubling property and Poincar´e inequality), we will be able to obtain some Liouville-type results. This chapter is based on the paper [GL03] by Guti´errez and Lanconelli. In the second chapter we treat some ultraparabolic equations on Lie groups. In this case RN is the support of a Lie group, and moreover we require that vector fields satisfy left invariance. After recalling some results of Cinti [Cin07] about this class of operators and associated potential theory, we prove a scalar convexity for mean-value operators of L-subharmonic functions, where L is our differential operator. In the third chapter we prove a necessary and sufficient condition of regularity, for boundary points, for Dirichlet problem on an open subset of RN related to sub-Laplacian. On a Carnot group we give the essential background for this type of operator, and introduce the notion of “quasi-boundedness”. Then we show the strict relationship between this notion, the fundamental solution of the given operator, and the regularity of the boundary points.

Mach bands and multiscale models of spatial vision:the role of first, second, and third derivative operators in encoding bars and edges

Ernst Mach observed that light or dark bands could be seen at abrupt changes of luminance gradient in the absence of peaks or troughs in luminance. Many models of feature detection share the idea that bars, lines, and Mach bands are found at peaks and troughs in the output of even-symmetric spatial filters. Our experiments assessed the appearance of Mach bands (position and width) and the probability of seeing them on a novel set of generalized Gaussian edges. Mach band probability was mainly determined by the shape of the luminance profile and increased with the sharpness of its corners, controlled by a single parameter (n). Doubling or halving the size of the images had no significant effect. Variations in contrast (20%-80%) and duration (50-300 ms) had relatively minor effects. These results rule out the idea that Mach bands depend simply on the amplitude of the second derivative, but a multiscale model, based on Gaussian-smoothed first- and second-derivative filtering, can account accurately for the probability and perceived spatial layout of the bands. A key idea is that Mach band visibility depends on the ratio of second- to first-derivative responses at peaks in the second-derivative scale-space map. This ratio is approximately scale-invariant and increases with the sharpness of the corners of the luminance ramp, as observed. The edges of Mach bands pose a surprisingly difficult challenge for models of edge detection, but a nonlinear third-derivative operation is shown to predict the locations of Mach band edges strikingly well. Mach bands thus shed new light on the role of multiscale filtering systems in feature coding. © 2012 ARVO.

Reducing MRI gradient coil vibration with rib stiffeners

This work investigates the effect of rib stiffeners on the free and forced vibration of a gradient coil in a Magnetic Resonance Imaging (MRI) scanner. Several reinforcement schemes are studied in this paper. One scheme utilizes the existing holes in the gradient coil structure (typically reserved for magnetic shims) to produce the reinforcement. Non-ferrous, non-magnetic carbon fibre rib stiffeners are employed to fill these holes in several ways to strengthen a gradient coil. Another scheme replaces the inner half of the gradient coil material with a grid of interconnected axial and circumferential rib stiffeners. It is found that the structural stiffness of the gradient coil increases substantially when the coil is reinforced by carbon fibre rib stiffeners. The reinforcement affects the noise and vibration response of the gradient coil structure in the following ways. It increases the frequency range of forced response of the gradient coil at low frequencies due to the increased resonant frequency of the fundamental mode of the coil. Secondly, it reduces the forced response amplitude of the coil structure (which is governed by the structural stiffness of the coil). Thirdly, it reduces the number of natural modes in the low and medium frequency range and therefore lessens the chance of the coil structure being excited resonantly by magnetic resonance signal acquisition sequences. It is shown that gradient coils modelled by solid finite element models have higher stiffness along the coil’s circumference and lower stiffness in the axial direction than those using shell finite element models.

Comparing subjective and objective measures of health : Evidence from hypertension for the income/health gradient

Economists rely heavily on self-reported measures to examine the relationship between income and health. We directly compare survey responses of a self-reported measure of health that is commonly used in nationally representative surveys with objective measures of the same health condition. We focus on hypertension. We find no evidence of an income/health greadient using self-reported hypertension but a sizeable gradient when using objectively measured hypertension. We also find that the probability of a false negative reporting is significantly income graded. Our results suggest that using commonly available self-reported chronic health measures might underestimate true income-related inequalities in health.

Lateral buckling strength of simply supported LiteSteel beams subject to moment gradient effects

The flexural capacity of of a new cold-formed hollow flange channel section known as LiteSteel beam (LSB) is limited by lateral distortional buckling for intermediate spans, which is characterised by simultaneous lateral deflection, twist and web distortion. Recent research has developed suitable design rules for the member capacity of LSBs. However, they are limited to a uniform moment distribution that rarely exists in practice. Many steel design codes have adopted equivalent uniform moment distribution factors to accommodate the effect of non-uniform moment distributions in design. But they were derived mostly based on the data for conventional hot-rolled, doubly symmetric I-beams subject to lateral torsional buckling. The effect of moment distribution for LSBs, and the suitability of the current steel design code rules to include this effect for LSBs are not yet known. This paper presents the details of a research study based on finite element analyses of the lateral buckling strength of simply supported LSBs subject to moment gradient effects. It also presents the details of a number of LSB lateral buckling experiments undertaken to validate the results of finite element analyses. Finally, it discusses the suitability of the current design methods, and provides design recommendations for simply supported LSBs subject to moment gradient effects.

The modulation of outdoor running speed : the influence of gradient

This thesis aimed to investigate the way in which distance runners modulate their speed in an effort to understand the key processes and determinants of speed selection when encountering hills in natural outdoor environments. One factor which has limited the expansion of knowledge in this area has been a reliance on the motorized treadmill which constrains runners to constant speeds and gradients and only linear paths. Conversely, limits in the portability or storage capacity of available technology have restricted field research to brief durations and level courses. Therefore another aim of this thesis was to evaluate the capacity of lightweight, portable technology to measure running speed in outdoor undulating terrain. The first study of this thesis assessed the validity of a non-differential GPS to measure speed, displacement and position during human locomotion. Three healthy participants walked and ran over straight and curved courses for 59 and 34 trials respectively. A non-differential GPS receiver provided speed data by Doppler Shift and change in GPS position over time, which were compared with actual speeds determined by chronometry. Displacement data from the GPS were compared with a surveyed 100m section, while static positions were collected for 1 hour and compared with the known geodetic point. GPS speed values on the straight course were found to be closely correlated with actual speeds (Doppler shift: r = 0.9994, p < 0.001, Δ GPS position/time: r = 0.9984, p < 0.001). Actual speed errors were lowest using the Doppler shift method (90.8% of values within ± 0.1 m.sec -1). Speed was slightly underestimated on a curved path, though still highly correlated with actual speed (Doppler shift: r = 0.9985, p < 0.001, Δ GPS distance/time: r = 0.9973, p < 0.001). Distance measured by GPS was 100.46 ± 0.49m, while 86.5% of static points were within 1.5m of the actual geodetic point (mean error: 1.08 ± 0.34m, range 0.69-2.10m). Non-differential GPS demonstrated a highly accurate estimation of speed across a wide range of human locomotion velocities using only the raw signal data with a minimal decrease in accuracy around bends. This high level of resolution was matched by accurate displacement and position data. Coupled with reduced size, cost and ease of use, the use of a non-differential receiver offers a valid alternative to differential GPS in the study of overground locomotion. The second study of this dissertation examined speed regulation during overground running on a hilly course. Following an initial laboratory session to calculate physiological thresholds (VO2 max and ventilatory thresholds), eight experienced long distance runners completed a self- paced time trial over three laps of an outdoor course involving uphill, downhill and level sections. A portable gas analyser, GPS receiver and activity monitor were used to collect physiological, speed and stride frequency data. Participants ran 23% slower on uphills and 13.8% faster on downhills compared with level sections. Speeds on level sections were significantly different for 78.4 ± 7.0 seconds following an uphill and 23.6 ± 2.2 seconds following a downhill. Speed changes were primarily regulated by stride length which was 20.5% shorter uphill and 16.2% longer downhill, while stride frequency was relatively stable. Oxygen consumption averaged 100.4% of runner’s individual ventilatory thresholds on uphills, 78.9% on downhills and 89.3% on level sections. Group level speed was highly predicted using a modified gradient factor (r2 = 0.89). Individuals adopted distinct pacing strategies, both across laps and as a function of gradient. Speed was best predicted using a weighted factor to account for prior and current gradients. Oxygen consumption (VO2) limited runner’s speeds only on uphill sections, and was maintained in line with individual ventilatory thresholds. Running speed showed larger individual variation on downhill sections, while speed on the level was systematically influenced by the preceding gradient. Runners who varied their pace more as a function of gradient showed a more consistent level of oxygen consumption. These results suggest that optimising time on the level sections after hills offers the greatest potential to minimise overall time when running over undulating terrain. The third study of this thesis investigated the effect of implementing an individualised pacing strategy on running performance over an undulating course. Six trained distance runners completed three trials involving four laps (9968m) of an outdoor course involving uphill, downhill and level sections. The initial trial was self-paced in the absence of any temporal feedback. For the second and third field trials, runners were paced for the first three laps (7476m) according to two different regimes (Intervention or Control) by matching desired goal times for subsections within each gradient. The fourth lap (2492m) was completed without pacing. Goals for the Intervention trial were based on findings from study two using a modified gradient factor and elapsed distance to predict the time for each section. To maintain the same overall time across all paced conditions, times were proportionately adjusted according to split times from the self-paced trial. The alternative pacing strategy (Control) used the original split times from this initial trial. Five of the six runners increased their range of uphill to downhill speeds on the Intervention trial by more than 30%, but this was unsuccessful in achieving a more consistent level of oxygen consumption with only one runner showing a change of more than 10%. Group level adherence to the Intervention strategy was lowest on downhill sections. Three runners successfully adhered to the Intervention pacing strategy which was gauged by a low Root Mean Square error across subsections and gradients. Of these three, the two who had the largest change in uphill-downhill speeds ran their fastest overall time. This suggests that for some runners the strategy of varying speeds systematically to account for gradients and transitions may benefit race performances on courses involving hills. In summary, a non – differential receiver was found to offer highly accurate measures of speed, distance and position across the range of human locomotion speeds. Self-selected speed was found to be best predicted using a weighted factor to account for prior and current gradients. Oxygen consumption limited runner’s speeds only on uphills, speed on the level was systematically influenced by preceding gradients, while there was a much larger individual variation on downhill sections. Individuals were found to adopt distinct but unrelated pacing strategies as a function of durations and gradients, while runners who varied pace more as a function of gradient showed a more consistent level of oxygen consumption. Finally, the implementation of an individualised pacing strategy to account for gradients and transitions greatly increased runners’ range of uphill-downhill speeds and was able to improve performance in some runners. The efficiency of various gradient-speed trade- offs and the factors limiting faster downhill speeds will however require further investigation to further improve the effectiveness of the suggested strategy.

Carbon pools and fluxes along an environmental gradient in northern Arizona

Carbon pools and fluxes were quantified along an environmental gradient in northern Arizona. Data are presented on vegetation, litter, and soil C pools and soil CO2 fluxes from ecosystems ranging from shrub-steppe through woodlands to coniferous forest and the ecotones in between. Carbon pool sizes and fluxes in these semiarid ecosystems vary with temperature and precipitation and are strongly influenced by canopy cover. Ecosystem respiration is approximately 50 percent greater in the more mesic, forest environment than in the dry shrub-steppe environment. Soil respiration rates within a site vary seasonally with temperature but appear to be constrained by low soil moisture during dry summer months, when approximately 75% of total annual soil respiration occurs. Total annual amount of CO2 respired across all sites is positively correlated with annual precipitation and negatively correlated with temperature. Results suggest that changes in the amount and periodicity of precipitation will have a greater effect on C pools and fluxes than will changes in temperature :in the semiarid Southwestern United States.