WO2019132783A1 - Method for assessing slip resistance of a surface - Google Patents

Method for assessing slip resistance of a surface Download PDF

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Publication number
WO2019132783A1
WO2019132783A1 PCT/SG2018/050643 SG2018050643W WO2019132783A1 WO 2019132783 A1 WO2019132783 A1 WO 2019132783A1 SG 2018050643 W SG2018050643 W SG 2018050643W WO 2019132783 A1 WO2019132783 A1 WO 2019132783A1
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image
images
micro
specular
roughness
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French (fr)
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Li Shen
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Agency For Science, Technology And Research
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01BMEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00Measuring arrangements characterised by the use of optical means
    • G01B11/30Measuring arrangements characterised by the use of optical means for measuring roughness or irregularity of surfaces
    • G01B11/303Measuring arrangements characterised by the use of optical means for measuring roughness or irregularity of surfaces using photoelectric detection means
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00Investigating or analysing materials by the use of optical means, i.e. using infra-red, visible or ultra-violet light
    • G01N21/17Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/55Specular reflectivity
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00Investigating or analysing materials by the use of optical means, i.e. using infra-red, visible or ultra-violet light
    • G01N21/17Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/55Specular reflectivity
    • G01N21/57Measuring gloss
    • G01N2021/575Photogoniometering
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2201/00Features of devices classified in G01N21/00
    • G01N2201/02Mechanical
    • G01N2201/022Casings
    • G01N2201/0221Portable; cableless; compact; hand-held

Abstract

Disclosed herein is method for assessing slip resistance of a surface. The method comprises capturing a plurality of images of the surface; determining a micro-facet normal distribution from the plurality of images; and constructing a one-dimensional (1-D) specular reflectance profile of the surface from the micro-facet normal distribution. One or more surface roughness properties is then inferred from the 1D specular reflectance profile.

Description

METHOD FOR ASSESSING SLIP RESISTANCE OF A SURFACE

TECHNICAL FIELD

[001] The present disclosure relates to a method for surface condition assessment and, more particularly, a method for assessing slip resistance of a surface. The method may be applied to, but is not limited to, surfaces on which people walk and other areas in which the smoothness of a surface can result in a slip hazard.

BACKGROUND

[002] A large proportion of workplace injuries result from slips. Slip assessment tools are therefore used to identify areas in the workplace that are prone to causing a slip hazard, to improve safety and help prevent injuries and accidents.

[003] Slip assessments generally rely on measuring floor surface roughness.

Conventional techniques to measure surface roughness rely on instruments - e.g. spectrometers - that require the measurement tool to be in close proximity to the surface being assessed. To position the tool therefore involves subjecting the user of the tool to an unknown surface condition. The safety of the user can thereby be put at risk.

[004] It is desirable therefore to provide a safer method of assessing surface condition that is more cost effective.

SUMMARY OF THE PRESENT DISCLOSURE

[005] Disclosed herein is a method for assessing slip resistance of a surface, the method comprising:

capturing a plurality of images of the surface;

determining a micro-facet normal distribution from the plurality of images; constructing a one-dimensional (1 -D) specular reflectance profile of the surface from the micro-facet normal distribution; and

inferring one or more surface roughness properties from the 1 D specular reflectance profile.

[006] The plurality of images may be captured at a half-angle θh of between 0 and p/2.

[007] The 1 D specular reflectance profile may be a 1 D specular bi-directional reflectance distribution function.

[008] The method may further comprise illuminating the surface during capturing of the plurality of images of the surface. [009] The plurality of images may be captured from different directions and from different viewing perspectives.

[010] The method may further comprise:

registering a first image of the plurality of images as a reference image, the first image having a first viewpoint;

identifying one or more pixels of the reference image in each other image of the plurality of images; and

reconstructing each image of the plurality of images, except the first image, at the first viewpoint.

[011] The first image may be an image taken normal to a plane of the surface.

[012] The specular reflectance profile may be constructed using the equation a minimum value of in a group being

Figure imgf000004_0002
Figure imgf000004_0001
Figure imgf000004_0004

being irradiance caused by flash lighting in an image, being incident

Figure imgf000004_0003

intensity of a light source.

[013] Each image of the plurality of images may be registered in a database, and wherein registering each image involves removing at least one of:

diffuse reflection components; and

colour factor.

[014] Inferring surface roughness properties may comprise comparing the micro facet normal distribution to one or more stored micro-facet normal distributions of materials of known surface roughness.

[015] Also disclosed herein is a system for assessing slip resistance of a surface, the system comprising:

an image capture device configured to capture a plurality of images of the surface; and

at least one data processor configured to:

determine a micro-facet normal distribution from the plurality of images;

construct a one-dimensional (1 -D) specular reflectance profile of the surface from the micro-facet normal distribution; and

infer one or more surface roughness properties from the 1 D specular reflectance profile.

[016] The image capture device may be configured to capture the plurality of images at half-angles θh of between 0 and p/2.

[017] The 1 D specular reflectance profile may be a 1 D specular bi-directional reflectance distribution function. [018] The system may further comprise a light source for illuminating the surface during capturing of the plurality of images of the surface, the light source being attached to the image capture device.

[019] The plurality of images may be captured from different directions and from different viewing perspectives.

[020] The data processor may be configured to:

register a first image of the plurality of images as a reference image, the first image having a first viewpoint;

identify one or more pixels of the reference image in each other image of the plurality of images; and

reconstruct each image of the plurality of images, except the first image, at the first viewpoint.

[021] The data processor may be configured to select for the reference image an image taken normal to a plane of the surface.

[022] The specular reflectance profile may be constructed using the equation a minimum value of in a group being

Figure imgf000005_0004
Figure imgf000005_0002
Figure imgf000005_0001

being irradiance caused by flash lighting in an image, being incident

Figure imgf000005_0003

intensity of a light source.

[023] The system may further comprise a database in which each image of the plurality of images is registered, and wherein the data processor is configured to remove at least one of:

diffuse reflection components; and

colour factor,

from each image before registering the respective image.

[024] The data processor may be configured to infer surface roughness properties by comparing the micro-facet normal distribution to one or more stored micro-facet normal distributions of materials of known surface roughness.

BRIEF DESCRIPTION OF THE DRAWINGS

[025] Some embodiments of systems and methods for assessing slip resistance of a surface, in accordance with present teachings, will now be described by way of non-limiting example only, with reference to the accompanying drawings in which:

Figure 1 illustrates methods for assessing slip resistance in accordance with some embodiments;

Figure 2 illustrates the parameters of a bi-directional reflectance distribution function applied to a surface; Figure 3 schematically depicts the surface of Figure 2, with a partial exploded and simplified illustration of a microsurface of the surface;

Figure 4 is a schematic depiction of an image capture device, such as a camera, with a light source attached thereto;

Figure 5 shows:

Figure 5(a) - the acquisition setup for a 1 D BRDF;

Figure 5(b) - the sample input images captured using only flash lighting;

Figure 5(c) - the sample input images under natural illumination and with flash lighting; and

Figure 5(d) - the sample input images under natural illumination without flash lighting;

Figure 6 shows 109 images of a sample of material captured from different viewpoints;

Figure 7 shows the input images of Figure 6, re-projected to the reference view with the recovered camera and 3D geometry information;

Figure 8 illustrates the process of surface normal recovery, in which:

Figure 8(a) shows one of the input images of tiles;

Figure 8(b) shows the recovered surface normals of the tiles of Figure 8(a); and

Figure 8(c) shows the recovered albedos for the tiles of Figure 8(a); Figure 9 shows pixel clustering results applied to two samples in which:

Figure 9(a) is the input images;

Figure 9(b) shows the pixel clustering in red-green-blue (RGB) space; and

Figure 9(c) shows the clustered pixels in different shades;

Figure 10 shows the recovered profile of another sample material;

Figure 1 1 shows the 1 -dimensional BRDF of 21 samples reconstructed under a single light source;

Figure 12 is a 1 -dimensional BRDF reconstruction under a single light source, in which:

Figure 12(a) a series of input images with flashing lighting;

Figure 12(b) recovered specular components of the images of Figure 12(a) with image colours inverted; and

Figure 12(c) reconstructed 1 -dimensional specular BRDF of the samples of Figure 12(a); Figure 13 is a 1 -dimensional BRDF reconstruction under natural illumination, in which:

Figure 13(a) shows the input images under flash lighting

Figure 13(b) shows the recovered specular component of the images taken per Figure 13(a) with image colour inverted; and

Figure 13(c) shows the reconstructed 1 -dimensional specular BRDF; Figure 14 shows 1 -dimensional BRDF profiles of 20 materials reconstructed under natural illumination;

Figure 15 is an example of images registered or stored in a BRDF database such as database 508 of Figure 5, there being 20 sample materials in the database each of which is represented by an image where the camera principal axis is coincident with the surface normal of the material sample under the flash light;

Figure 16 shows examples of 1 -dimensional BRDF profiles of several materials reconstructed with a single point light source; and

Figure 17 shows examples of 1 -dimensional BRDF profiles of various samples of materials reconstructed under natural lighting.

DETAILED DESCRIPTION

[026] Embodiments of the present method and system for assessing slip resistance of a surface can be used to improve workplace safety, by identifying slip and trip hazards. These methods may also be used to assess the viability of particular materials for surfaces on which people may walk. Further, these methods may be useful where it is desirable to control movement of one object relative to another in a mechanical system, in which understanding the slip resistance of a surface can assist in inhibiting or, conversely, enabling relative movement of those objects.

[027] It has been determined that materials of a surface can be distinguished by examining their reflectance properties. This concept is extended by the method 100 of Figure 1 , for assessing slip resistance of a surface. The method 100 broadly comprises:

Step 102: capturing a plurality of images;

Step 104: determining a micro-facet normal distribution;

Step 106: constructing a specular reflectance profile;

Step 108: inferring one or more surface roughness properties from the 1 D specular reflectance profile.

[028] Step 102 involves capturing multiple images. The images may be captured using any suitable image capture device such as a camera, smartphone gonioreflectometer and the like. An arrangement 400 for achieving image capture according to step 102 is schematically depicted in Figure 4.

[029] Using such an arrangement 400, the camera 402 and light source or illumination device 404 can be shifted to vary the relative angles between the incident light from the light source 404 and the light reflected in the direction of the aperture of the camera 402.

[030] Step 104 involves determining a micro-facet normal distribution from the plurality of images. In this regard, the specular BRDF employed for determining physical model slip resistance - as opposed to computer graphics models - is based on micro-facet theory. Micro-facet theory assumes surface geometry is much larger than the wavelengths of the incoming light.

[031] In micro-facet models, a surface is composed of many micro-facets. Each micro-facet, for a surface that is not perfectly smooth, will present a reflectance normal that differs from the reflectance normal of a smooth surface. The degree to which the normal differs can be used to infer surface roughness.

[032] The micro-facet normal distribution describes how micro-facet normals are distributed around half-vector h of l and v over the micro-surface. Flence, D(h) , as set out in formula 2, describes the roughness of a surface. For very smooth surfaces such as mirrors or silvered surfaces, with the uniform m = n, D(h ) can be expected to perform as a delta function with a sharp peak at the mirror direction h = n. For very rough surfaces with large variance of m, D(h ) can be expected near constant. In other words, the greater the roughness the more uniform the distribution of reflected surface radiance from an incident beam. Consequently, the roughness of a surface can be inferred from its BRDF.

[033] Step 106 involves constructing a specular reflectance profile.

Advantageously, some embodiments of the present methods enable a one dimensional (1 -D) specular reflectance profile of the surface to be constructed from the plurality of images or the micro-facet normal distribution, yet without loss of necessary resolution or information from which slip resistance can be assessed.

[034] Steps 104, 106 and 108 are based on the understanding that materials of a surface can be distinguished by examining their reflectance properties. These reflectance properties are characterised by the Bi-directional Reflectance Distribution Function (BRDF).

[035] A BRDF defines how light is reflected at an opaque surface. The BRDF takes a vector for the incoming light direction, a vector for the outgoing light direction, and returns the ratio of reflected radiance exiting along the incoming light direction to the irradiance incident on the surface from the outgoing light direction. [036] BRDFs are thus represented as 4-dimensional (4D) functions of the incident lighting direction, and reflected lighting direction, with two

Figure imgf000009_0003
Figure imgf000009_0005

dimensions for each of the vectors, as shown in Figure 2. For a Lambertian (perfectly diffuse) surface, the BRDF is constant, i.e. There is no specular

Figure imgf000009_0004

component of the BRDF for the surface. Flowever, for most surfaces, the BRDF consists of both the diffuse and the specular components

Figure imgf000009_0006

[037] Under global illumination, the irradianc e l on the surface x observed at the viewing direction v can be computed by summing up the incident illumination L(Z) from every direction on the hemisphere W:

Figure imgf000009_0001

where n is the surface normal at x.

[038] In micro-facet models, each micro-facet is assumed to only reflect light in a single direction according to its normal (m). This is shown in Figure 3, in which the BRDF variables are diagrammatically shown as incident vectors I, n and h on a surface 300, and a partial exploded view 302 of a portion of the surface 300 is shown with micro-facets the normals for which are indicated by respective vectors m.

[039] The specular BRDF based on micro-facet theory can be written as:

Figure imgf000009_0002
where n is the surface normal, G is a geometry term of shadow masking between micro-facets, F is the Fresnel reflectance term which describes the amount of light that reflects from a mirror surface given the material index of refraction, and D(h) is the micro-facet normal distribution.

[040] BRDFs can be measured directly from real objects using calibrated cameras and light sources. Flowever, it is very time consuming to capture the whole 4D function This is because establishing an image for all relevant angles

Figure imgf000009_0007

between the surface, light source and image capture device is time-consuming and, computationally, resource intensive.

[041] The method 100 was, in-part, developed on the discovery that BRDFs of many real materials exhibit strong symmetry and redundancy. Such symmetry and redundancy includes isotropy, reciprocity, half-vector symmetry, etc. It can therefore be possible to safely reduce the BRDF domain without loss of information that would otherwise make the method unreliable. [042] In general, it is considered that the locations of the light source and camera or image capture device should be independently varied. This ensures independent selective variation of the angle of incidence and reflectance can be achieved, and the camera can then capture images of radiance at a wide variety of angles for each incident angle.

[043] While the above process of independent variation of camera and light source angles is very thorough, it is highly time-consuming and computationally expensive. In contrast, an arrangement shown in Figure 4 can be used, in which images are captured with a light attached to the camera. The light source is arranged such that the direction of emission of light from the light source is substantially coincident with the surface normal of the aperture of the image capture device. Using this arrangement, the incident and outgoing lighting directions are coincident, i.e. / = v, or sufficiently coincident to enable an assessment of surface roughness.

[044] Thus, the half-vector h - i.e. the direction halfway between the view direction and the light position - overlaps with the viewing angle v, and θd - the angle between the half-angle and the incident light direction - is always 0. By moving the camera around and thus making identical movements of the light source, images with q - angle between the surface normal and the half-vector - varying over the range of [0,p/2] can be captured. This 1 -dimensional (1 D) BRDF approximation covers the full dynamic range of θh . Therefore, such as 1 D BRDF faithfully captures the characteristics of the micro-facet D(h ) function, per step 106 of Figure 1 .

[045] The surface roughness can be inferred from the 1 D BRDF profile per step 108. Specifically, this 1 D BRDF approximation psh ) allows us to capture the important properties of specular reflectance, e.g. the strength and extent of specular lobes, which strongly depends on the micro-facet normal distribution term D(h ) . Slippery surfaces can be identified by utilizing the 1 D BRDF profiles: psh) with sharp specular peaks should belong to smooth surfaces.

[046] Using a 1 D BRDF, the time and computational requirements to compute surface roughness are dramatically reduced when compared with existing methods. Moreover, the equipment required to capture and process images is greatly simplified. Thus, the present methods can be used to efficiently and cost-effectively asses slip resistance of a surface. Similarly, as shown in step 1 18 of Figure 1 - shown in broken lines as it can be optional in some embodiments - the method 100 may be used in a method of identifying a slippery condition of the surface.

[047] As mentioned with reference to Figure 1 , the method 100 of assessing slip resistance of a surface of a material involves capturing a plurality of images of the surface of the material - step 102 - and constructing a one-dimensional (1 D) specular reflectance profile of the surface from the plurality of images - step 102. Step 102 can involve attaching a light source to the camera, or otherwise moving the light source such that the incident light vector is substantially coincident with the viewing direction and thus also with the half-angle. Doing so substantially reduces computational complexity while allowing faithful reproduction of the relevant characteristics of the micro-facet function. The method 100 further comprises determining a micro-facet normal distribution from the 1 D specular reflectance profile - step 106. Surface roughness properties may then be inferred from the 1 D specular reflectance profile - step 108.

[048] In some embodiments, ambient lighting or global illumination may be sufficient to enable measurement of the radiance. In other aspects, as shown with reference to Figure 4 and step 1 10 of Figure 1 , the image acquisition step 102 may involve illuminating the surface of the material with a light source 404. The images may then be captured using a handheld camera 402 at various directions of illumination and various viewpoints. The images are then registered.

[049] Notably, where the method 100 involves registering (i.e. storing in a database) images, a first image or reference image may be identified - step 1 12. For example, one or more pixels may be identified in the reference image - step 1 14— that are then identified in the other captured images. By identifying the pixels in the other images, a series of images can be reconstructed - step 1 16 - so that all of the reconstructed images show the material oriented in a common orientation but having the reflectance of the material as acquired from different viewpoints - see, for example, Figure 7.

[050] Figure 5(a) shows the data capture setup, or system 500 for assessing slip resistance of a surface, and some sample images are shown in Figures 5(b), (c) and (d). The system 500 employed an image capture device embodied by a stand- mounted camera 502 configured to capture a plurality of images of the surface being assessed. Presently, the camera 502 was set up to capture images of a tile sample 504 on an indexed plate 506. The images captured by the camera 502 may be registered (i.e. stored) in the camera itself, or in a database 508 which may be locally located as shown, or remotely located.

[051] Before or after registration, a data processor 510 - of which there may be more than one - processes the images. In that regard, the data processor 510 is configured to construct a 1 D specular reflectance profile of the surface from the plurality of images, determine a micro-facet normal distribution from the 1 D specular reflectance profile - in particular a 1 D specular bi-directional reflectance distribution function - and infer one or more surface roughness properties from the micro-facet normal distribution component. As discussed above, the image capture device 502 is configured to capture the plurality of images at half-angles θh of between 0 and p/2.

[052] The light source 504 is arranged to illuminate the surface during capturing of the plurality of images of the surface, and is attached to the camera 502 to ensure the incident direction and viewing direction are aligned.

[053] To reduce memory consumption and to improve computational efficiency, each image captured by the camera 502 is registered in database 508, and the data processor 510 removes at least one of:

diffuse reflection components; and

colour factor,

from each image before registering the respective image.

[054] The reflectance values of the registered images are therefore colour agnostic, which reduces the effect of colour variations between samples of like slip resistance.

[055] The data processor 510 then infers surface roughness properties by comparing the micro-facet normal distribution of the newly sampled images to one or more stored micro-facet normal distributions of materials of known surface roughness. Thus, the surface roughness of the newly sampled material can be determined by reference to the known surface roughness of previously sampled materials.

[056] The camera was a handheld camera and the light source was a handheld flashlight, though other cameras and light sources can be used as appropriate. Desirably, the light source 504 will be attached to the camera 502 to ensure consistent relative orientation between the two.

[057] Multiple images of each sample tile 504 were captured under varying illumination/view directions. The incident flash lighting direction is densely sampled over the upper hemisphere defined by the sample material’s surface normal, n per Figure 3. In one example, the images were captured at 109 different viewpoints - the 109 viewpoints resulted from the use of 6 different camera/light source heights, 18 directions at each height, and one at the normal direction. The normal direction may be used as the reference frame per step 1 12 of Figure 1 .

[058] Since the camera/lighting positions are known, 3-dimensional (3D) geometry of the tile can be recovered to facilitate image registration. The view where the sample material is most front-to-parallel to the camera - i.e. closest to a position at which the surface normal of the material is also normal to the centre of the aperture of the image capture device - is taken as the reference view. The 3D position of each pixel is projected in the canonical image to the other images to collect multiple observations captured at the different viewpoints. Thus, pixels are identified in the reference image. These pixels may be arbitrarily selected or may be selected to be distinct features such as corners or edges of the material, transitions between different types of surface on the material and so forth. Each of these pixels is then identified in the other images to enable the images to be displayed from a common orientation but with the radiance as detected from the particular orientation from which the respective image was captured - see Figure 7.

[059] Where the reconstructed images are missing pixels due to the material taking up a smaller proportion of the aperture in images taken at an angle when compared with images taken along the surface normal, the missing pixels may be inserted by averaging or interpolating between surrounding pixels and padding where missing pixels are adjacent an edge.

[060] Figure 6 shows examples of the 109 input images taken in the scheme described above, using the assembly of Figure 5, on a sample material (Sample #1 ). The re-projected or reconstructed images are shown in Figure 7. Using or considering pixels (i.e. the light-emitting diode (LED) representative of each pixel) as known point-like distant light sources, the surface normal n(x) at each point can be recovered by the photometric stereo technique. Consequently, the albedo - the proportion of incident light that is reflected by a surface - at each point pd(x) can be recovered.

[061] Figure 8 shows the recovered normal and albedo results of another set of sample materials, identified as Sample #13 and #16. Figure 8 illustrates how the recovered surface normal and albedos can be produced for materials even with highly irregular surface characteristics. Figures 8(a) shows the input images of the samples or tiles. Figures 8(b) show the recovered surface normal for each of the input samples. Even for the highly irregular surface of the lower sample in Figure 8, the surface normal recovery is almost complete. Figures 8(c) show the recovered albedos.

[062] Figure 9 demonstrates a clustering method applied to group pixels of the same material as those used for the sampling shown in Figure 8, in RGB space according to the albedo values. From the recorded image irradiance /, a 1 D specular BRDF profile of the material for each group can be constructed according to the following equation:

Figure imgf000013_0001
where the minimum value of pd(x) in this group is considered as is the
Figure imgf000014_0001

irradiance at x caused by the flash lighting in the th image. is the incident

Figure imgf000014_0002

intensity of the flash light source. The recovered specular BRDF can be considered as a distinguishing feature for identifying smooth/slippery surfaces.

[063] In the examples discussed above, a database (e.g. database 508) of 1 D surface (reflectance) profiles of a material can be generated. The profiles are based on acquired or captured images in a controlled environment and/or under natural lighting conditions. The profiles may be modified prior to, or while in, storage. For example, each image of the plurality of images may be registered and the data processor may be configured to remove at least one of:

diffuse reflection components; and

colour factor,

from each image before registering the respective image, or while that image is in storage.

[064] The database 508 can be analysed under a laboratory setting to validate that 1 D BRDF profiles can be used to identify slippery/smoothing surfaces. In the laboratory setting, the images of the tile samples are captured in a dark room where the flash light is the only light source. The 1 D reflectance profile can be recovered directly from the recorded pixel intensity

Figure imgf000014_0003

[065] Figure 1 1 shows the recovered profiles of 20 materials. These profiles result from reconstruction under a single light source. The θh range of 1 ~10 degrees corresponds to the specular phenomena (e.g. specular reflection). It is observed that the samples with a smooth surface (Sample #13, #20) have strong and sharp specular peaks. Figure 12 illustrates a few samples with different specular BRDF profiles. Samples #20 and #13 have a strong and sharp specular peak as shown on the left hand side of the respective profiles in Figure 12(c), whereas Sample #4 has only a moderate peak. Contrastingly, Sample #16 has the lowest specular peak of the 20 materials analysed, for which profiles were reconstructed per Figure 1 1 .

[066] Table 1 shows the roughness indices of the 20 materials obtained by using a roughness tester (Surtronic S-100). The results based on the methods discussed herein, such as method 100, are consistent with the readings recorded by the roughness meter. The experiments outlined above further show that the BRDF profiles form a discriminative feature for each material. Moreover, the experiments show the surface smoothness can be determined from the proposed 1 D BRDF profiles that allow slip resistance of a floor surface to be assessed.

Figure imgf000015_0001

Table 1 shows examples of roughness indices of various materials

[067] Using the experimental techniques outlined above, and the methods described herein and with reference to the Figures, a surface BRDF database - such as database 508 - with the properties of various surface materials under a single point source can be generated. Examples of profiles of various materials are shown in Figures 15 to 17.

[068] In the various examples, the BRDF database has removed the diffuse reflection components and colour factor. The database of profiles can therefore be applied readily to materials with different colour. In other words, the selective removal of information from some of the profiles does not restrict the applicability of the database in assessing slip resistance of surfaces and, in fact, may extend the use of the database by enabling colour to be disregarded.

[069] Figure 10 shows an example that demonstrates the generality of the BRDF database, and applied to an unknown sample, identified as Sample #23. In the example, the sample material was assessed to have a smooth surface according to its BRDF profile by comparing that profile with the known profiles in the BRDF database.

[070] Any number of images may be used to assess slip resistance of a surface. As set out in an example above, 109 images were used. In other embodiments, four to five input images of the surface of the material are captured at random positions, including one image taken at the normal direction. These four to five images are adequate to recover the 1 D BRDF profile.

[071] In various embodiments, the images are captured under natural lighting conditions, with and without flash light for each direction. If (x, v) can be recovered from the image pair with and without flash light. Similarly, the 3D geometry and registered the images can be recovered. To recover the surface normal, any conventional method for recovering dense surface normals under arbitrary unknown illumination from the registered image set can be used. The BRDF profile can then be recovered according to Equation 1 with If (x, v).

[072] Figure 14 shows the profiles of the 20 materials recovered under natural lighting. The results of a few samples are further illustrated in Figure 13, which shows samples having strong and sharp specular peaks, moderate specular component, and weak specular component.

[073] Figure 15 illustrates an example of BRDF database of 20 sample materials.

The images are captured when the principal axis of the camera - e.g. the axis normal to the centre of the aperture - is coincident with the surface normal of the material sample under the flash light or other light source.

[074] Figure 16 illustrates an example of 1 -dimensional BRDF profiles of several materials reconstructed with single point source. Notably, the recovery results under natural light are consistent with those recovered under a single lighting source.

[075] Examples of profiles recovered under natural lighting are shown in Figure 17.

[076] Various of the aforementioned embodiments are applicable in methods for vision-based slip resistance measurement of a surface, surface deformation or surface condition monitoring.

[077] Many modifications will be apparent to those skilled in the art without departing from the scope of the present invention.

[078] Throughout this specification, unless the context requires otherwise, the word "comprise", and variations such as "comprises" and "comprising", will be understood to imply the inclusion of a stated integer or step or group of integers or steps but not the exclusion of any other integer or step or group of integers or steps.

Claims

1. A method for assessing slip resistance of a surface, the method comprising:
capturing a plurality of images of the surface;
determining a micro-facet normal distribution from the plurality of images; constructing a one-dimensional (1 -D) specular reflectance profile of the surface from the micro-facet normal distribution; and
inferring one or more surface roughness properties from the 1 D specular reflectance profile.
2. The method of claim 1 , wherein the plurality of images is captured at a half-angle θh of between 0 and π/2.
3. The method of claim 1 or 2, wherein the 1 D specular reflectance profile is a 1 D specular bi-directional reflectance distribution function.
4. The method of any preceding claim, further comprising illuminating the surface during capturing of the plurality of images of the surface.
5. The method of any preceding claim, wherein the plurality of images are captured from different directions and from different viewing perspectives.
6. The method of any preceding claim, further comprising:
registering a first image of the plurality of images as a reference image, the first image having a first viewpoint;
identifying one or more pixels of the reference image in each other image of the plurality of images; and
reconstructing each image of the plurality of images, except the first image, at the first viewpoint.
7. The method of claim 6, wherein the first image is an image taken normal to a plane of the surface.
8. The method of any preceding claim, wherein the specular reflectance profile is constructed using the equation a minimum value of
Figure imgf000017_0001
Figure imgf000017_0002
in a group being being irradiance caused by flash lighting in an image,
Figure imgf000017_0003
Figure imgf000017_0004
and being incident intensity of a light source.
9. The method of any preceding claim, wherein each image of the plurality of images is registered in a database, and wherein registering each image involves removing at least one of:
diffuse reflection components; and
colour factor.
10. The method of any preceding claim, wherein inferring surface roughness properties comprises comparing the micro-facet normal distribution to one or more stored micro facet normal distributions of materials of known surface roughness.
1 1 . A system for assessing slip resistance of a surface, the system comprising:
an image capture device configured to capture a plurality of images of the surface; and
at least one data processor configured to:
determine a micro-facet normal distribution from the plurality of images;
construct a one-dimensional (1 -D) specular reflectance profile of the surface from the micro-facet normal distribution; and
infer one or more surface roughness properties from the 1 D specular reflectance profile.
12. The system of claim 1 1 , wherein the image capture device is configured to capture the plurality of images at half-angles θh of between 0 and p/2.
13. The system of claim 1 1 or 12, wherein the 1 D specular reflectance profile is a 1 D specular bi-directional reflectance distribution function.
14. The system of any one of claims 1 1 to 13, further comprising a light source for illuminating the surface during capturing of the plurality of images of the surface, the light source being attached to the image capture device.
15. The system of any one of claims 1 1 to 14, wherein the plurality of images are captured from different directions and from different viewing perspectives.
16. The system of any one of claims 1 1 to 15, wherein the data processor is configured to: register a first image of the plurality of images as a reference image, the first image having a first viewpoint;
identify one or more pixels of the reference image in each other image of the plurality of images; and
reconstruct each image of the plurality of images, except the first image, at the first viewpoint.
17. The system of claim 16, wherein the data processor is configured to select for the reference image an image taken normal to a plane of the surface.
18. The system of any one of claims 1 1 to 17, wherein the specular reflectance profile is constructed using the equation a minimum value of
Figure imgf000019_0001
Figure imgf000019_0002
in a group being being irradiance caused by flash lighting in an image,
Figure imgf000019_0004
Figure imgf000019_0003
and being incident intensity of a light source.
19. The system according to any one of claims 1 1 to 18, further comprising a database in which each image of the plurality of images is registered, and wherein the data processor is configured to remove at least one of:
diffuse reflection components; and
colour factor,
from each image before registering the respective image.
20. The system according to any one of claims 1 1 to 19, wherein the data processor is configured to infer surface roughness properties by comparing the micro-facet normal distribution to one or more stored micro-facet normal distributions of materials of known surface roughness.
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