A moment-based technique for the automatic spatial alignment of plantar pressure data

A convolutional neural network Cascade for plantar pressure images registration

BACKGROUND

Plantar pressure image (PPI) recorded in high spatial and temporal resolution is very useful in clinical gait analysis. For functional analysis of PPI, image registration is often performed to maximally correlate source image with a template image. Previous methods estimate the registration parameters by iteratively optimizing different objective functions. These methods are often computational expensive to achieve satisfactory registration accuracy.

RESEARCH QUESTION

Can we develop a single PPI registration technique that performs more rapidly than previous methods, and that also maintains adequate PPI correspondence as defined by various (dis)similarity metrics?

METHODS

A cascaded convolutional neural network (CNN) was proposed for the registration of PPIs. Our model was trained to learn a regression from the difference between the template and misaligned images to the registration parameters. The registration performance was evaluated by three different metrics, i.e. the mean squared error (MSE), the exclusive or (XOR), and the mutual information (MI). For comparison, four previous methods were also implemented. These included the principal axes (PA) method, the center of pressure trajectory (COP) method, the MSE method, and the XOR method.

RESULTS

Experimental results on a dataset with 71 PPI template-source pairs showed that the proposed CNN-based method could obtain comparable registration accuracy to the MSE and XOR method. With regards to the registration speed, registration durations (mean ± sd in seconds) per image pair were: MSE (30.584 ± 2.171), XOR (24.245 ± 1.596), PA (0.016 ± 0.003), COP (25.614 ± 0.341), and the proposed model (0.054 ± 0.007).

SIGNIFICANCE

Our findings indicate that the proposed registration approach can achieve high accuracy but less computational time. Thus, it is more practical to utilize our pre-trained CNN-based model to develop near-real time applications for plantar pressure images registration.

Spatial resolution in plantar pressure measurement revisited

Plantar pressures are typically measured using sensors of finite area, so the accuracy with which one can measure true maximum pressure is dependent on sensor size. Measurement accuracy has been modeled previously for one patient's metatarsals (Lord, 1997), but has not been modeled either for general subjects or for other parts of the foot. The purposes of this study were (i) to determine whether Lord's (1997) model is also valid for heel and hallux pressures, and (ii) to examine how sensor size relates to measurement accuracy in the context of four factors common to many measurement settings: pressure pulse size, foot positioning, pressure change quantification, and gross pressure redistribution. Lord's (1997) model was first generalized and was then validated using 10 healthy walking subjects, with relatively low RMSE values on the order of 20 kPa. Next, postural data were used to show that gross pressure redistributions can be accurately quantified (p<0.002), even with rather gross sensor sizes of 30 mm. Finally, numerical analyses revealed that the relation between sensor size and measurement accuracy is highly complex, with deep dependency on the measurement context. In particular, the critical sensor widths required to achieve 90% accuracy ranged from 1.7 mm to 17.4 mm amongst the presently investigated scenarios. Since measurement accuracy varies so extensively with so many factors, the current results cannot yield specific recommendations regarding spatial resolution. It is concluded simply that no particular spatial resolution can yield a constant measurement accuracy across common plantar pressure measurement tasks.

Registration of plantar pressure images

In this work, five computational methodologies to register plantar pressure images are compared: (1) the first methodology is based on matching the external contours of the feet; (2) the second uses the phase correlation technique; (3) the third addresses the direct maximization of cross-correlation using the Fourier transform; (4) the fourth minimizes the sum of squared differences using the Fourier transform; and (5) the fifth methodology iteratively optimizes an intensity (dis)similarity measure based on Powell's method. The accuracy and robustness of the five methodologies were assessed by using images from three common plantar pressure acquisition devices: a Footscan system, an EMED system, and a light reflection system. Using the residual error as a measure of accuracy, all methodologies revealed to be very accurate even in the presence of noise. The most accurate was the methodology based on the iterative optimization, when the mean squared error was minimized. It achieved a residual error inferior to 0.01 mm and 0.6 mm for non-noisy and noisy images, respectively. On the other hand, the methodology based on image contour matching was the fastest, but its accuracy was the lowest.

Gait recognition: highly unique dynamic plantar pressure patterns among 104 individuals

Everyone's walking style is unique, and it has been shown that both humans and computers are very good at recognizing known gait patterns. It is therefore unsurprising that dynamic foot pressure patterns, which indirectly reflect the accelerations of all body parts, are also unique, and that previous studies have achieved moderate-to-high classification rates (CRs) using foot pressure variables. However, these studies are limited by small sample sizes (n < 30), moderate CRs (CR ≃ 90%), or both. Here we show, using relatively simple image processing and feature extraction, that dynamic foot pressures can be used to identify n = 104 subjects with a CR of 99.6 per cent. Our key innovation was improved and automated spatial alignment which, by itself, improved CR to over 98 per cent, a finding that pointedly emphasizes inter-subject pressure pattern uniqueness. We also found that automated dimensionality reduction invariably improved CRs. As dynamic pressure data are immediately usable, with little or no pre-processing required, and as they may be collected discreetly during uninterrupted gait using in-floor systems, foot pressure-based identification appears to have wide potential for both the security and health industries.

Nonlinear spatial warping for between-subjects pedobarographic image registration

Foot size and shape vary between individuals and the foot adopts arbitrary stance phase postures, so traditional pedobarographic analyses regionalize foot pressure images to afford homologous data comparison. An alternative approach that does not require explicit anatomical labelling and that is used widely in other functional imaging domains is to register images such that homologous structures optimally overlap and then to compare images directly at the pixel level. Image registration represents the preprocessing cornerstone of such pixel-level techniques, so its performance warrants independent attention. The purpose of this study was to evaluate the performance of four between-subjects warping registration algorithms including: Principal Axes (PA), four-parameter Optimal Scaling (OS4), eight-parameter Optimal Projective (OP8), and locally affine Nonlinear (NL). Fifteen subjects performed 10 trials of self-paced walking, and their peak pressure images were registered within-subjects using an optimal rigid body transformation. The resulting mean images were then registered between-subjects using all four methods in all 210 (15x14) subject combinations. All registration methods improved alignment, and each method performed qualitatively well for certain image pairs. However, only the NL consistently performed satisfactorily because of disproportionate anatomical variation in toe lengths and rearfoot/forefoot width, for example. Using three independent image (dis)similarity metrics, MANOVA confirmed that the NL method yielded superior registration performance (p<0.001). These data demonstrate that nonlinear spatial warping is necessary for robust between-subject pedobarographic image registration and, by extension, robust homologous data comparison at the pixel level.