Dynamic DistanceBased Shape Features for Gait Recognition
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Abstract
We propose a novel skeletonbased approach to gait recognition using our Skeleton Variance Image. The core of our approach consists of employing the screened Poisson equation to construct a family of smooth distance functions associated with a given shape. The screened Poisson distance function approximation nicely absorbs and is relatively stable to shape boundary perturbations which allows us to define a rough shape skeleton. We demonstrate how our Skeleton Variance Image is a powerful gait cycle descriptor leading to a significant improvement over the existing state of the art gait recognition rate.
Keywords
Smoothed distance function Rough skeletons Gait recognition Skeleton Variance Image1 Introduction

We introduce the concept of the Skeleton Variance Image and demonstrate that it stores important information about moving human silhouette figures. We show that the Skeleton Variance Image is a powerful gait cycle descriptor which leads us to a significant improvement over the existing state of the art gait recognition rate.

We demonstrate that smooth distance fields yield robust extraction of rough skeletal structures which promote stability with respect to shape boundary perturbations.

In particular, we demonstrate that solving the socalled screened Poisson equation yields a computationally efficient way to define a family of smooth distance functions with simple and efficient control over their smoothness yielding a skeleton which is significantly more robust compared to the exact distance function.
1.1 Gait Recognition
Gait recognition seeks to identify a person by their walking manner and posture [45]. With applications including surveillance and access control, gait as a behavioural biometric is advantageous over physical biometrics, e.g. fingerprint, given capture without consent or cooperation, unobtrusively, at low resolution and at distance. Early studies in medical [48] and psychophysics [15] demonstrate the uniqueness of gait, and gait recognition has developed significantly since the first computerbased approach by Niyogi and Adelson [49] in 1994. In practical terms, we require robustness to real world covariate factors capable of altering gait appearance and motion which are detrimental to performance, e.g. clothing, bags, shoe type and even elapsed time between capture.
Approaches are split into modelbased, modelfree and multiinformation fusion. Modelbased approaches [41, 72] construct gait signatures by modelling or tracking human body segments via anthropometrics [17, 19], modelfree approaches [27, 28] disregard human body structure in favour of silhouettebased representations, while multiinformation fusion approaches replicate human vision perception by utilising multiple features [40, 69] or biometrics e.g. face [32, 35]. We currently consider single feature and biometric gait recognition, however this is not to say the performance of our proposed approach could be boosted with such efforts; we also find the benefits of low computational cost and image quality insensitivity associated with modelfree approaches outweigh the benefits of view and scale invariance associated with modelbased approaches.
Considering modelfree approaches more in detail, silhouettes commonly serve as the foundation and can be extracted easily from sources such as time of flight, Microsoft Kinect and Lidar; colour and texture are rejected thus ensuring no bias to appearance occurs during gait recognition given motion is more consistent over time.
Skeleton, compared to silhouette, gait representations are few and far between—especially those founded on distance functions. Lack of implementation is linked to boundary perturbation sensitivity from imperfectly extracted silhouettes and the natural self occluding nature of gait. For example, an oversimplified skeleton can be constructed by connecting the silhouette figure centroid to its head and limbs [13], whereas anthropometrics enable a more realistic six joint skeleton [72]. Both examples utilise a gait cycles worth of skeletons which is uneconomical with respect to memory and computational costs; the alternative is to perform the increasingly popular space and timenormalisation techniques to yield a single, compact 2D gait representation [6, 27, 33, 68, 71, 74].
1.2 Generalised Distance Fields and DistanceBased Shape Features
A generalised distance field is a scalar (vector) field approximating the minimum distance (minimum distance and direction) to a shape with respect to a certain metric. Generalised distance fields and distancerelated shape features such as skeletons [9] are widely used in pure mathematics in relation to analysis of Hamilton–Jacobi equations and curvaturedriven manifold evolutions [1, 43], computational mathematics [50] in connection to level set methods, computer vision, pattern recognition, and image processing [23, 24, 25, 54, 76], shape matching [51], computer graphics and geometric modeling [11, 14, 34, 52, 53], computational mechanics [21], CFD and turbulence modelling [66] (the socalled wall distance, the minimum distance to a solid wall is a key parameter in several turbulence models), medical image processing, analysis, and visualisation [36], and many other areas.
Our gait recognition approach deals with smooth distance fields approximated by solutions to the Poisson equation alongside its normalised and screened Poisson equations; results suggest our approach yields an efficient manner of extracting rough shape skeletons associated with the smooth distance fields. Given a sequence of silhouettes representing a gait cycle, the pixelwise variance of their corresponding skeletons reflect dynamic gait patterns which turns out to be a powerful gait descriptor.
1.3 Validation
Validation of our proposed approach is performed on the largest, latest and most covariate factor rich, standardised publicly available database: TUM Gait from Audio, Image and Depth (GAID). Overall, our representation significantly boosts robustness as we focus on gait motion which is more consistent over time than gait appearance.
2 Smooth Distance Functions
It is well known that the true Euclidean distance function and its corresponding skeleton (medial axis) are very sensitive to small boundary perturbations. In our study, imperfect silhouette segmentation leads to an abundance of boundary noise. As a possible remedy, one can hope that a properly defined smoothed distance function and its corresponding skeleton are less sensitive to segmentation inaccuracies and silhouette boundary noise. Below we exploit a partial differential equation (PDE) approach and consider several PDEbased schemes to generating smooth distance functions.
To the best of our knowledge, the idea of using diffusiontype PDEs for skeleton extraction purposes was first proposed in [64] where the socalled screened Poisson equations were used. While we consider some other PDEdriven schemes for the distance function approximation and skeleton extraction, the screened Poisson equations serve as our main working horse.
2.1 Screened Poisson Distance Function
Our first approach to constructing a family of smooth distance functions explores an asymptotic relationship between the distance function and solutions to screened Poisson equations [67, Theorem 2.3].
Distance function approximation (3) has been previously employed to extract skeletal structures from grayscale images [64]. An inhomogeneous version of the screened Poisson equation in (1) has been employed [26, 56] to estimate the distance function from a point set. An anisotropic version of (1) was used very recently [14] for tracing geodesics on triangulated surfaces.
It is interesting that the energy corresponding to (1) is a part of the AmbrosioTortorelli elliptic regularisation [2] of the MumfordShah functional [47]. See also, for example, [57] and [5, Sect. 4.2].
2.2 Screened Poisson Distance and Mean Curvature Flow
In the twodimensional case an interesting relationship between \(v({\varvec{x}})\), the solution to (1), and its level set curvature was derived in [64] and utilised for grayscale image skeletonisation purposes. Below we informally extend the relationship to the multidimensional case.
2.3 Poisson and Normalised Poisson Distance Functions
Poisson distance functions have been employed for action recognition [24, 25], skeleton extraction [4], turbulence modelling applications [65], and geometric defeaturing purposes [70].
Both the Poisson and normalised Poisson distance functions have lower computational costs compared to the screened Poisson distance functions (1, 3). On the other hand, the latter provides us with an ability to control the amount of smoothing by tuning parameter \(t\) in (1). For example, as shown in the right of Fig. 2, for a sufficiently small \(t\), the screened Poisson distance function delivers a better approximation of true distance \(d({\varvec{x}},\partial \varOmega )\) than the normalised Poisson and Poisson distance functions.
2.4 \(p\)Laplacian Distance Functions and \(L_p\!\) Distance Fields
It is also worth mentioning that the socalled \(L_p\)distance fields introduced recently in [7] also allow the user to control an amount of smoothing added to the true distance function. However, according to our numerical experiments, the screened Poisson distance functions tend to distribute smoothing uniformly over the domain, while the \(L_p\)distance fields apply less smoothing near the boundary and more smoothing far from the boundary.
3 Rough Skeletons
After the pioneering work of Blum [9], skeletonbased shape representations have been widely utilised for the analysis and processing of static and dynamic 2D and 3D shapes [59]. Strong correlations between medial shape structures and perceptual shape organisation [38, 39] remain a subject of intensive research [3].
While the classical medial axis [9] reflects shape organisation, its main drawback is high sensitivity to smallscale boundary perturbations. As the medial axis of an object is closely connected to the distance function from the boundary of the object (the medial axis can be defined as the set of singularities of the distance function), it is natural to expect that a smooth distance function may lead to a more robust shape skeletonisation scheme. Indeed attempts of using smooth distance functions for better (less sensitive) skeletonisation have been made, for example in [4, 18, 25, 64].
Note that in contrast to the classical medial axis, our rough skeleton is not a deformation retract of the original shape. For example, the rough skeleton shown in Fig. 8 contains gaps while the silhouette is a simple connected 2D shape. If necessary, Canny’s hysteresis thresholding procedure [12] can be utilised to remove such gaps.
4 Skeleton Variance Image
Over a complete gait cycle, skeleton motion can be extracted by considering how pixel intensity values vary during the skeleton sequence; this prompts our primary contribution—Skeleton Variance Image (SVIM) gait representation.
5 Experimental Procedure
5.1 Validation
5.2 Baseline and Comparable Representations
The Gait Energy Image (GEI) [27], seen in the leftmost column of Fig. 9, is our baseline and applies the same procedures outlined in Sect. 4 however using the pixelwise mean and silhouettes in place of the pixelwise variance and skeletons respectively. This appearancebased representation permits visualisation of static and dynamic information corresponding to high and low pixel intensity values respectively. We also present two new related representations for enhanced comparison: Skeleton Energy Image (SEIM) and Gait Variance Image (GVI) seen in the middle left and middle right columns of Fig. 9 respectively. The SEIM and GVI are analogous to SVIM and GEI respectively where the pixelwise mean replaces the pixelwise variance and vice versa respectively. These representations permits equal comparison of appearancebased (GEI and SEIM) vs. motionbased (GVI and SVIM) representations as well as silhouette (GEI and GVI) vs. skeleton (SEIM and SVIM) representations.
5.3 Distance Function
We compare the behaviour of distance functions extracted via the Poisson and screened and normalised Poisson equations.
5.4 Smoothing Parameter
Given smoothing parameter \(t\) dictates the skeleton thickness produced by the screened Poisson distance function, demonstrated in Fig. 7, we therefore choose a broad range of values to evaluate its effect on gait recognition: small values {t = 0.1, 0.5, 5} correspond to a thinner, more traditional looking skeleton compared to large values {t = 10–90 in steps of 10} which correspond to a thicker skeleton tending towards a silhouette appearance.
5.5 Dimensionality Reduction and Classification
The GEI, GVI, SEIM and SVIM serve as a means to represent gait (\(128\times 178\)—typical for the TUM GAID database [31]) and describe gait when reshaped to a 1D feature vector (22784D). Dimensionality reduction transforms the feature vector into lower dimensional space (154D) by maximising variance and class separability with Principle Component Analysis (PCA) and Linear Discriminant Analysis (LDA) respectively [42]. Nearest Neighbour classification utilises the cosine distance measure [31] where rank 1 and rank 5 results are presented demonstrating the correct identity occurring first or in the top five matches respectively. This dimensionality reduction and classification combination is commonly employed by approaches utilising single, compact 2D gait representations like our baseline [27], and is advantageous in situations where training sequences are few.
6 Results and Discussion
6.1 Smoothing Parameter \(t\) Behaviour
We are currently interested in the weighted average performance as we desire \(t\) which is most effective over a varying range of covariate factors. First to notice is the significant performance jump, regardless of covariate factor, from \(t=0.1\) to \(t=0.5\) which is attributed to \(t=0.1\) producing an overly thin skeleton risking considerable segmentation at branch points especially. Weighted average performance wise, we can see a subtle performance trend where the SVIM and SEIM decrease and increase respectively with larger \(t\) values; this is linked to the SVIM and SEIM preferring a thinner, more traditional looking skeleton compared to a thicker skeleton tending towards a skeleton appearance respectively. We therefore suggest small (\(t = 5\)) value for the SVIM, however as pointed to us by one of the reviewers of the paper, scaling the image \(\varOmega \) by a factor \(s\) (while keeping its resolution fixed) and assuming that the solution \(v(x)\) to (1) remains invariant leads to scaling the smoothing parameter \(t\) by \(s^2\). This means that in our current model no optimal \(t\) exists if the image size and resolution are not specified—note that \(t\) may also be database dependent.
6.2 Comparison to GEI Baseline
TUM GAID database rank 1 and rank 5 performance for representations: GEI (baseline), and SEIM, GVI and SVIM, and sequences: normal (N), carrying a bag (B), shoes (S), time and normal (TN), time and carrying a bag (TB), time and shoes (TS), weighted average; distance functions are based on: Poisson, normalised Poisson and screened Poisson schemes
Approach (Rank 1 %)  N  B  S  TN  TB  TS  Weighted average  

Appearance  GEI (baseline)  99.7  19.0  96.5  34.4  0.0  43.8  67.4 
SEIM (Poisson)  97.4  8.1  89.7  40.6  3.1  28.1  61.2  
SEIM (normalised Poisson)  99.0  18.4  96.1  15.6  3.1  28.1  66.0  
SEIM (screened Poisson  \(t=0.5\))  96.1  8.7  84.8  21.9  0.0  18.8  58.6  
SEIM (screened Poisson  \(t=5\))  98.4  14.8  88.7  28.1  0.0  34.4  63.0  
SEIM (screened Poisson  \(t=50\))  99.0  17.7  93.9  28.1  0.0  28.1  65.4  
Motion  GVI  99.0  47.7  94.5  62.5  15.6  62.5  77.3 
SVIM (Poisson)  97.4  53.6  88.1  65.6  21.9  53.1  76.6  
SVIM (normalised Poisson)  98.4  54.2  92.9  50.0  28.1  37.5  77.8  
SVIM (screened Poisson  \(t=0.5\))  98.1  63.9  86.8  62.5  34.4  50.0  79.7  
SVIM (screened Poisson  \(t=5\))  98.4  64.2  91.6  65.6  31.3  50.0  81.4  
SVIM (screened Poisson  \(t=50\))  97.7  51.9  93.9  59.4  37.5  53.1  78.3 
Approach (Rank 5 %)  N  B  S  TN  TB  TS  Weighted average  

Appearance  GEI (baseline)  99.7  33.5  97.7  46.9  9.4  50.0  73.1 
SEIM (Poisson)  99.4  15.8  93.6  46.9  6.3  46.9  66.2  
SEIM (normalised Poisson)  99.7  32.6  98.7  34.4  6.3  37.5  72.2  
SEIM (screened Poisson  \(t=0.5\))  98.1  16.5  91.6  31.3  0.0  34.4  64.3  
SEIM (screened Poisson  \(t=5\))  99.7  26.1  93.2  37.5  6.3  50.0  69.1  
SEIM (screened Poisson  \(t=50\))  99.7  35.2  96.8  37.5  12.5  43.8  72.9  
Motion  GVI  99.0  63.9  95.8  75.0  31.3  75.0  83.8 
SVIM (Poisson)  98.1  72.6  92.6  75.0  37.5  78.1  85.5  
SVIM (normalised Poisson)  99.0  73.6  95.5  71.9  43.8  71.9  86.8  
SVIM (screened Poisson  \(t=0.5\))  99.4  82.6  94.8  75.0  46.9  71.9  89.7  
SVIM (screened Poisson  \(t=5\))  99.4  79.4  94.8  75.0  53.1  65.6  88.7  
SVIM (screened Poisson  \(t=50\))  98.1  70.0  94.5  78.1  50.0  68.8  85.5 
6.3 Covariate Factor Performance Trends
Normal (N) and shoe (S) sequences perform highly given their appearance similarities to training sequences. Note the shoe sequences cause little gait appearance and motion alterations, whereas shoe types such as heels and flip flops may cause greater alterations and subsequently cause increased misclassification [10]. Bag carrying (B) sequences show poorer performances given the significant appearance alterations caused; bags appear as a mass of pixels around the back or a bend in silhouettes and skeletons respectively, see Fig. 9—note that bags also cause the body to lean due to compensation for a shifted centre of gravity. Timebased sequences (TN, TB, TS) cause significant issues performance wise, halving performance in some cases; see [46] for further information regarding time as a covariate factor during gait recognition. The primary cause of misclassification is due to appearance alterations caused by clothing which is a hidden covariate factor given the time (months) between capture. Clothing as a covariate factor is often addressed separately e.g. in the CASIA B database [73, 75]. Overall, these trends apply to both appearancebased and motionbased, and silhouette and skeleton approaches.
6.4 Appearance vs. MotionBased Representations
We can see significant performance differences between appearancebased and motionbased representations across the database. Especially during timebased sequences, motionbased representations often double that achieved with appearancebased representations—this occurs given gait motion is considerably more consistent over time compared to gait appearance. This observation leads us to recommend motionbased representations given their ability to overcome the majority and especially more complex real world covariate factors presented by the database.
6.5 Silhouette vs. Skeleton Representations
A pattern exists where combining silhouette and appearancebased representations (GEI) is favourable while skeleton and motionbased representations (SVIM) is superior overall, therefore this is what we recommend for gait recognition. The SVIM is successful as it places emphasis on body motion as opposed to covariate factor motion; for example, a rucksack undergoes motion due to natural gait motion (visible especially in the GVI in Fig. 9), where the skeleton represents the rucksack as a mere bend in the skeleton compared to a mass of static and dynamic pixel values for silhouette representations.
6.6 Distance Function Behaviour
While the distance function constructed from the normalised Poisson provides performance increases over the Poisson, we find the screened Poisson superior and is advantageous given the tunable smoothing parameter \(t\) which provides a performance boost. With respect to time, the Poisson distance function is the fastest and the normalised and screened Poisson are successively slower to implement. However given our gait recognition approach is not geared towards realtime processing, we favour the screened Poisson for its superior person discrimination.
6.7 General Recommendations
We have demonstrated the variance aspect of our SVIM to be a useful tool during gait recognition given gait motion is more consistent over time compared to gait appearance. The SVIM paired with the screened Poisson distance function offers significant flexibility due to the tunable smoothing parameter \(t\). Note that we only suggest a general recommendation for smoothing parameter \(t\) instead of promoting an optimised parameter explicitly due to how performance changes with (a) silhouette quality e.g. missing head or limbs due to imperfect extraction, (b) silhouette creation i.e. RGB versus depth images, (c) image size, (d) databases and even (e) applications. While this means we could achieve greater performance with alternative smoothing parameters \(t\), we have none the less demonstrated the effectiveness of the SVIM with the screened Poisson distance function.
7 Comparison to State of the Art
Existing versus proposed TUM GAID database performances: normal (N), carrying a bag (B), shoes (S), time and normal (TN), time and carrying a bag (TB), time and shoes (TS), weighted average
8 Conclusion and Future Work
We have demonstrated an efficient approach to extract skeletons via the screened Poisson equation with tunable smoothing parameter \(t\). This combined with skeleton and motionbased representations yields our proposed SVIM which is capable of superior covariate factor generalisation despite the tough timebased covariate factors posed by the TUM GAID database. The SVIM owes its success due to (a) utilising gait motion which is more consistent over time than gait appearance and (b) skeletons which place emphasis on gait motion as opposed to covariate factor motion for greater covariate factor handling compared to silhouettesbased representations. Future work considers extension to action recognition combined with more advanced learning and classification tools (e.g. SVM).
Notes
Acknowledgments
We would like to thank the anonymous reviewers for extensively reading this paper and providing their valuable and constructive feedback. Tenika Whytock is supported by an EPSRC DTA studentship. Neil M. Robertson is supported by the MOD University Defence Research Collaboration in Signal Processing (EPSRC grant number EP/J015180/1).
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