Location distribution of randomly acquired characteristics on a shoe sole.

Footwear comparison is used to link between a suspect's shoe and a shoeprint found at a crime scene. Forensic examiners compare the two items, and the conclusion reached is based on class characteristics and randomly acquired characteristics (RACs), such as scratches or holes. An important question concerns the distribution of the location of RACs on shoe soles, which can serve as a benchmark for comparison. This study examines the probability of observing RACs in different areas of a shoe sole using a database of approximately 13,000 RACs observed on 386 outsoles. The analysis is somewhat complicated as the shoes are differentiated by shape and contact surface, and the RACs' locations are subject to measurement errors. A method that takes into account these challenges is presented. All impressions are normalized to a standardized axis to allow for inter-comparison of RACs on outsoles of different sizes and contact areas, and RACs are localized to one of 14 subareas of the shoe sole. Expected frequencies in each region are assumed to be Poisson distributed with rate parameters that depend on the subarea and the contact surface. Three different estimation approaches are studied: a naive crude approach, a shoe-specific random effects model, and an estimate that is based on conditional maximum likelihood. It is shown that the rate is not uniform across the shoe sole and that RACs are approximately twice as likely to appear at certain locations, corresponding to the foot's morphology. The results can guide investigators in determining a shoeprint's evidential value.

Dataset of Digitized RACs and Their Rarity Score Analysis for Strengthening Shoeprint Evidence.

In recent years, there is a growing demand to fortify the scientific basis of forensic methodology. During 2016, the President's Council of Advisors on Science and Technology (PCAST) published a report that states there are no appropriate empirical studies that support the foundational validity of footwear analysis to associate shoeprints with particular shoes based on specific identifying marks, which is a basic scientific demand from the field. Furthermore, meaningful databases that can support such studies do not exist. Without such databases, statistical presentation of the comparison results cannot be fulfilled either. In this study, a database of over 13,000 randomly acquired characteristics (RACs) such as scratches, nicks, tears, and holes, as they appear on shoe sole test impressions, from nearly 400 shoe soles was collected semi-automatically. The location, orientation, and the contour of each RAC were determined for all the RACs on each test impression. The statistical algorithm Statistic Evaluation of Shoeprint Accidentals (SESA) was developed to calculate a score for finding another feature similar to a particular scanned and digitized RAC in the same shape, location, and orientation as the examined one. A correlation was found between the results of SESA and the results of real casework, strengthening our belief in the ability of SESA to assist the expert in reaching a conclusion while performing casework. The score received at the end of the process serves the expert as a guiding number, allowing more objective and accurate results and conclusions.

Inherent variation in multiple shoe-sole test impressions.

Shoeprints left at crime scenes are seldom perfect. Many prints are distorted or contaminated by various materials. Noisy background often contributes to vagueness on the shoeprints as well. Test impressions made from the suspect's shoes in the laboratory are considered a genuine replication of the shoe-sole. This naïve attitude is far from being correct. Consecutive test impressions made in the laboratory under strict similar conditions revealed differences among the exemplars of the same sole. Some of them are minor, but some are major, and can mislead the less experienced practitioners during the comparison process. This article focuses on the inherent within source variability between controlled shoeprints made from the same shoe, as it appears on the RACs. To describe and analyze this variability, repeated test impressions were prepared, and datasets were created. Several RACs were marked on each test impression, using an expert assisting software tool (developed in the authors' lab). The variance in repeated test impressions is demonstrated and possible sources are discussed. This variance should be considered when trying to establish the degree of matching between individual characteristics.

Dependence among randomly acquired characteristics on shoeprints and their features.

Randomly acquired characteristics (RACs), also known as accidental marks, are random markings on a shoe sole, such as scratches or holes, that are used by forensic experts to compare a suspect's shoe with a print found at the crime scene. This article investigates the relationships among three features of a RAC: its location, shape type and orientation. If these features, as well as the RACs, are independent of each other, a simple probabilistic calculation could be used to evaluate the rarity of a RAC and hence the evidential value of the shoe and print comparison, whereas a correlation among the features would complicate the analysis. Using a data set of about 380 shoes, it is found that RACs and their features are not independent, and moreover, are not independent of the shoe sole pattern. It is argued that some of the dependencies found are caused by the elements of the sole. The results have important implications for the way forensic experts should evaluate the degree of rarity of a combination of RACs.

Kinematic decomposition and classification of octopus arm movements.

The octopus arm is a muscular hydrostat and due to its deformable and highly flexible structure it is capable of a rich repertoire of motor behaviors. Its motor control system uses planning principles and control strategies unique to muscular hydrostats. We previously reconstructed a data set of octopus arm movements from records of natural movements using a sequence of 3D curves describing the virtual backbone of arm configurations. Here we describe a novel representation of octopus arm movements in which a movement is characterized by a pair of surfaces that represent the curvature and torsion values of points along the arm as a function of time. This representation allowed us to explore whether the movements are built up of elementary kinematic units by decomposing each surface into a weighted combination of 2D Gaussian functions. The resulting Gaussian functions can be considered as motion primitives at the kinematic level of octopus arm movements. These can be used to examine underlying principles of movement generation. Here we used combination of such kinematic primitives to decompose different octopus arm movements and characterize several movement prototypes according to their composition. The representation and methodology can be applied to the movement of any organ which can be modeled by means of a continuous 3D curve.

Nearly automatic motion capture system for tracking octopus arm movements in 3D space.

Tracking animal movements in 3D space is an essential part of many biomechanical studies. The most popular technique for human motion capture uses markers placed on the skin which are tracked by a dedicated system. However, this technique may be inadequate for tracking animal movements, especially when it is impossible to attach markers to the animal's body either because of its size or shape or because of the environment in which the animal performs its movements. Attaching markers to an animal's body may also alter its behavior. Here we present a nearly automatic markerless motion capture system that overcomes these problems and successfully tracks octopus arm movements in 3D space. The system is based on three successive tracking and processing stages. The first stage uses a recently presented segmentation algorithm to detect the movement in a pair of video sequences recorded by two calibrated cameras. In the second stage, the results of the first stage are processed to produce 2D skeletal representations of the moving arm. Finally, the 2D skeletons are used to reconstruct the octopus arm movement as a sequence of 3D curves varying in time. Motion tracking, segmentation and reconstruction are especially difficult problems in the case of octopus arm movements because of the deformable, non-rigid structure of the octopus arm and the underwater environment in which it moves. Our successful results suggest that the motion-tracking system presented here may be used for tracking other elongated objects.

Analyzing octopus movements using three-dimensional reconstruction.

Octopus arms, as well as other muscular hydrostats, are characterized by a very large number of degrees of freedom and a rich motion repertoire. Over the years, several attempts have been made to elucidate the interplay between the biomechanics of these organs and their control systems. Recent developments in electrophysiological recordings from both the arms and brains of behaving octopuses mark significant progress in this direction. The next stage is relating these recordings to the octopus arm movements, which requires an accurate and reliable method of movement description and analysis. Here we describe a semiautomatic computerized system for 3D reconstruction of an octopus arm during motion. It consists of two digital video cameras and a PC computer running custom-made software. The system overcomes the difficulty of extracting the motion of smooth, nonrigid objects in poor viewing conditions. Some of the trouble is explained by the problem of light refraction in recording underwater motion. Here we use both experiments and simulations to analyze the refraction problem and show that accurate reconstruction is possible. We have used this system successfully to reconstruct different types of octopus arm movements, such as reaching and bend initiation movements. Our system is noninvasive and does not require attaching any artificial markers to the octopus arm. It may therefore be of more general use in reconstructing other nonrigid, elongated objects in motion.

Dynamic model of the octopus arm. II. Control of reaching movements.

The dynamic model of the octopus arm described in the first paper of this 2-part series was used here to investigate the neural strategies used for controlling the reaching movements of the octopus arm. These are stereotypical extension movements used to reach toward an object. In the dynamic model, sending a simple propagating neural activation signal to contract all muscles along the arm produced an arm extension with kinematic properties similar to those of natural movements. Control of only 2 parameters fully specified the extension movement: the amplitude of the activation signal (leading to the generation of muscle force) and the activation traveling time (the time the activation wave takes to travel along the arm). We found that the same kinematics could be achieved by applying activation signals with different activation amplitudes all exceeding some minimal level. This suggests that the octopus arm could use minimal amplitudes of activation to generate the minimal muscle forces required for the production of the desired kinematics. Larger-amplitude signals would generate larger forces that increase the arm's stability against perturbations without changing the kinematic characteristics. The robustness of this phenomenon was demonstrated by examining activation signals with either a constant or a bell-shaped velocity profile. Our modeling suggests that the octopus arm biomechanics may allow independent control of kinematics and resistance to perturbation during arm extension movements.

Dynamic model of the octopus arm. I. Biomechanics of the octopus reaching movement.

The octopus arm requires special motor control schemes because it consists almost entirely of muscles and lacks a rigid skeletal support. Here we present a 2D dynamic model of the octopus arm to explore possible strategies of movement control in this muscular hydrostat. The arm is modeled as a multisegment structure, each segment containing longitudinal and transverse muscles and maintaining a constant volume, a prominent feature of muscular hydrostats. The input to the model is the degree of activation of each of its muscles. The model includes the external forces of gravity, buoyancy, and water drag forces (experimentally estimated here). It also includes the internal forces generated by the arm muscles and the forces responsible for maintaining a constant volume. Using this dynamic model to investigate the octopus reaching movement and to explore the mechanisms of bend propagation that characterize this movement, we found the following. 1) A simple command producing a wave of muscle activation moving at a constant velocity is sufficient to replicate the natural reaching movements with similar kinematic features. 2) The biomechanical mechanism that produces the reaching movement is a stiffening wave of muscle contraction that pushes a bend forward along the arm. 3) The perpendicular drag coefficient for an octopus arm is nearly 50 times larger than the tangential drag coefficient. During a reaching movement, only a small portion of the arm is oriented perpendicular to the direction of movement, thus minimizing the drag force.

How to move with no rigid skeleton? The octopus has the answers.

The octopus is amazingly flexible and shows exceptional control and coordination in all its movements. It seems remarkable to us skeletal creatures that the octopus achieves all this without a single bone.