Marshall's Lemma for Convex Density Estimation

Marshall's (1970) lemma is an analytical result which implies root-n-consistency of the distribution function corresponding to the Grenander (1956) estimator of a non-decreasing probability density. The present paper derives analogous results for the setting of convex densities on [0,\infty).

The First Density Estimation of an Isolated Eurasian Lynx Population in Southwest Asia

During November 2010–February 2011, we used camera traps to estimate the population density of Eurasian lynx Lynx lynx in Ciglikara Nature Reserve, Turkey, an isolated population in southwest Asia. Lynx density was calculated through spatial capture—recapture models. In a sampling eff ort of 1093 camera trap days, we identifi ed 15 independent individuals and estimated a density of 4.20 independent lynx per 100 km2, an unreported high density for this species. Camera trap results also indicated that the lynx is likely to be preying on brown hare Lepus europaeus, which accounted for 63% of the non-target species pictured. As lagomorph populations tend to fl uctuate, the high lynx density recorded in Ciglikara may be temporary and may decline with prey fl uctuation. Therefore we recommend to survey other protected areas in southwestern Turkey where lynx is known or assumed to exist, and continuously monitor the lynx populations with reliable methods in order to understand the populations structure and dynamics, defi ne sensible measures and management plans to conserve this important species.

Spatially-Explicit Testing of a General Aboveground Carbon Density Estimation Model in aWestern Amazonian Forest Using Airborne LiDAR

Mapping aboveground carbon density in tropical forests can support CO2 emissionmonitoring and provide benefits for national resource management. Although LiDAR technology has been shown to be useful for assessing carbon density patterns, the accuracy and generality of calibrations of LiDAR-based aboveground carbon density (ACD) predictions with those obtained from field inventory techniques should be intensified in order to advance tropical forest carbon mapping. Here we present results from the application of a general ACD estimation model applied with small-footprint LiDAR data and field-based estimates of a 50-ha forest plot in Ecuador?s Yasuní National Park. Subplots used for calibration and validation of the general LiDAR equation were selected based on analysis of topographic position and spatial distribution of aboveground carbon stocks. The results showed that stratification of plot locations based on topography can improve the calibration and application of ACD estimation using airborne LiDAR (R2 = 0.94, RMSE = 5.81 Mg?C? ha?1, BIAS = 0.59). These results strongly suggest that a general LiDAR-based approach can be used for mapping aboveground carbon stocks in western lowland Amazonian forests.

KDENS: Stata module for univariate kernel density estimation

kdens produces univariate kernel density estimates and graphs the result. kdens supplements official Stata's kdensity. Important additions are: adaptive (i.e. variable bandwidth) kernel density estimation, several automatic bandwidth selectors including the Sheather-Jones plug-in estimator, pointwise variability bands and confidence intervals, boundary correction for variables with bounded domain, fast binned approximation estimation. Note that the moremata package, also available from SSC, is required.

Using kernel density estimation to understand the influence of neighbourhood destinations on BMI

OBJECTIVES: Little is known about how the distribution of destinations in the local neighbourhood is related to body mass index (BMI). Kernel density estimation (KDE) is a spatial analysis technique that accounts for the location of features relative to each other. Using KDE, this study investigated whether individuals living near destinations (shops and service facilities) that are more intensely distributed rather than dispersed, have lower BMIs.

STUDY DESIGN AND SETTING: A cross-sectional study of 2349 residents of 50 urban areas in metropolitan Melbourne, Australia.

METHODS: Destinations were geocoded, and kernel density estimates of destination intensity were created using kernels of 400, 800 and 1200 m. Using multilevel linear regression, the association between destination intensity (classified in quintiles Q1(least)-Q5(most)) and BMI was estimated in models that adjusted for the following confounders: age, sex, country of birth, education, dominant household occupation, household type, disability/injury and area disadvantage. Separate models included a physical activity variable.

RESULTS: For kernels of 800 and 1200 m, there was an inverse relationship between BMI and more intensely distributed destinations (compared to areas with least destination intensity). Effects were significant at 1200 m: Q4, β -0.86, 95% CI -1.58 to -0.13, p=0.022; Q5, β -1.03 95% CI -1.65 to -0.41, p=0.001. Inclusion of physical activity in the models attenuated effects, although effects remained marginally significant for Q5 at 1200 m: β -0.77 95% CI -1.52, -0.02, p=0.045.

CONCLUSIONS: This study conducted within urban Melbourne, Australia, found that participants living in areas of greater destination intensity within 1200 m of home had lower BMIs. Effects were partly explained by physical activity. The results suggest that increasing the intensity of destination distribution could reduce BMI levels by encouraging higher levels of physical activity.

Scene invariant crowd counting

This paper describes a scene invariant crowd counting algorithm that uses local features to monitor crowd size. Unlike previous algorithms that require each camera to be trained separately, the proposed method uses camera calibration to scale between viewpoints, allowing a system to be trained and tested on different scenes. A pre-trained system could therefore be used as a turn-key solution for crowd counting across a wide range of environments. The use of local features allows the proposed algorithm to calculate local occupancy statistics, and Gaussian process regression is used to scale to conditions which are unseen in the training data, also providing confidence intervals for the crowd size estimate. A new crowd counting database is introduced to the computer vision community to enable a wider evaluation over multiple scenes, and the proposed algorithm is tested on seven datasets to demonstrate scene invariance and high accuracy. To the authors' knowledge this is the first system of its kind due to its ability to scale between different scenes and viewpoints.

Scene invariant crowd counting and crowd occupancy analysis

In public places, crowd size may be an indicator of congestion, delay, instability, or of abnormal events, such as a fight, riot or emergency. Crowd related information can also provide important business intelligence such as the distribution of people throughout spaces, throughput rates, and local densities. A major drawback of many crowd counting approaches is their reliance on large numbers of holistic features, training data requirements of hundreds or thousands of frames per camera, and that each camera must be trained separately. This makes deployment in large multi-camera environments such as shopping centres very costly and difficult. In this chapter, we present a novel scene-invariant crowd counting algorithm that uses local features to monitor crowd size. The use of local features allows the proposed algorithm to calculate local occupancy statistics, scale to conditions which are unseen in the training data, and be trained on significantly less data. Scene invariance is achieved through the use of camera calibration, allowing the system to be trained on one or more viewpoints and then deployed on any number of new cameras for testing without further training. A pre-trained system could then be used as a ‘turn-key’ solution for crowd counting across a wide range of environments, eliminating many of the costly barriers to deployment which currently exist.

Probability density function estimation using orthogonal forward regression

Using the classical Parzen window estimate as the target function, the kernel density estimation is formulated as a regression problem and the orthogonal forward regression technique is adopted to construct sparse kernel density estimates. The proposed algorithm incrementally minimises a leave-one-out test error score to select a sparse kernel model, and a local regularisation method is incorporated into the density construction process to further enforce sparsity. The kernel weights are finally updated using the multiplicative nonnegative quadratic programming algorithm, which has the ability to reduce the model size further. Except for the kernel width, the proposed algorithm has no other parameters that need tuning, and the user is not required to specify any additional criterion to terminate the density construction procedure. Two examples are used to demonstrate the ability of this regression-based approach to effectively construct a sparse kernel density estimate with comparable accuracy to that of the full-sample optimised Parzen window density estimate.

Crowd Counting Using Multiple Local Features

In public venues, crowd size is a key indicator of crowd safety and stability. Crowding levels can be detected using holistic image features, however this requires a large amount of training data to capture the wide variations in crowd distribution. If a crowd counting algorithm is to be deployed across a large number of cameras, such a large and burdensome training requirement is far from ideal. In this paper we propose an approach that uses local features to count the number of people in each foreground blob segment, so that the total crowd estimate is the sum of the group sizes. This results in an approach that is scalable to crowd volumes not seen in the training data, and can be trained on a very small data set. As a local approach is used, the proposed algorithm can easily be used to estimate crowd density throughout different regions of the scene and be used in a multi-camera environment. A unique localised approach to ground truth annotation reduces the required training data is also presented, as a localised approach to crowd counting has different training requirements to a holistic one. Testing on a large pedestrian database compares the proposed technique to existing holistic techniques and demonstrates improved accuracy, and superior performance when test conditions are unseen in the training set, or a minimal training set is used.

Crowd counting using group tracking and local features

In public venues, crowd size is a key indicator of crowd safety and stability. In this paper we propose a crowd counting algorithm that uses tracking and local features to count the number of people in each group as represented by a foreground blob segment, so that the total crowd estimate is the sum of the group sizes. Tracking is employed to improve the robustness of the estimate, by analysing the history of each group, including splitting and merging events. A simplified ground truth annotation strategy results in an approach with minimal setup requirements that is highly accurate.

Urban traffic state estimation: Fusing point and zone based data

Loop detectors are the oldest and widely used traffic data source. On urban arterials, they are mainly installed for signal control. Recently state of the art Bluetooth MAC Scanners (BMS) has significantly captured the interest of stakeholders for exploiting it for area wide traffic monitoring. Loop detectors provide flow- a fundamental traffic parameter; whereas BMS provides individual vehicle travel time between BMS stations. Hence, these two data sources complement each other, and if integrated should increase the accuracy and reliability of the traffic state estimation. This paper proposed a model that integrates loops and BMS data for seamless travel time and density estimation for urban signalised network. The proposed model is validated using both real and simulated data and the results indicate that the accuracy of the proposed model is over 90%.

Nonparametric Bayesian Density Modeling with Gaussian Processes

We present the Gaussian process density sampler (GPDS), an exchangeable generative model for use in nonparametric Bayesian density estimation. Samples drawn from the GPDS are consistent with exact, independent samples from a distribution defined by a density that is a transformation of a function drawn from a Gaussian process prior. Our formulation allows us to infer an unknown density from data using Markov chain Monte Carlo, which gives samples from the posterior distribution over density functions and from the predictive distribution on data space. We describe two such MCMC methods. Both methods also allow inference of the hyperparameters of the Gaussian process.