systems and methods for performing machine vision using diffuse structured light are provided . in accordance with some embodiments , specularities and shadows can be reduced in a machine vision system by using a two - dimensional light pattern that is diffuse along one of the two dimensions . one way to achieve such an illumination pattern is by placing an optical diffuser 202 in the path of projected illumination , as illustrated in fig2 a . in some embodiments , the diffuser can be linear , in that it scatters incident light substantially only along one dimension ( e . g ., dimension x 206 ) of its two spatial dimensions ( e . g ., dimension x 206 and dimension y 208 ). as shown in fig2 a , a single light ray 204 incident on the top of diffuser 202 can be converted into a one - dimensional fan of rays 210 that emerge from the bottom of diffuser 202 . the shape of fan 210 , which is determined by the scattering function d ( θ ) of diffuser 202 , can be chosen based on the needs of the application . in some embodiments , the scattering function can be wide and uniform . in some embodiments , diffuser 202 can be implemented as refractive elements with random surface profiles . these surfaces can be created using random physical processes such as sandblasting and holographic exposure , or can be created programmatically using a lithographic or direct writing method . in fig2 b , a plane of collimated light rays 212 incident upon a linear diffuser 202 in accordance with some embodiments is illustrated . the set of one - dimensional rays 212 is converted by the diffuser into a two - dimensional illumination field 214 . because the diffuser is linear , the illumination rays can ideally remain confined to the plane of incidence in accordance with some embodiments . this illumination field can be viewed as a set of coincident collimated light planes with a continuum of directions . as will be apparent to one of ordinary skill in the art , a linear diffuser that is intended to diffuse light in an intended dimension may in fact diffuse some light ( typically a small amount ) in an unintended dimension other than the intended dimension . such unintended diffusion may occur , for example , due to limits in engineering the diffuser . it should be understood that the term “ linear diffuser ” as used herein is intended to cover diffusers that perfectly diffuse in only one dimension as well as diffusers the substantially diffuse in only one dimension while also diffusing slightly in one or more other dimensions . the effect of the diffuse illumination is illustrated in fig3 . while point p 110 of fig1 receives a single light ray , point p 310 of fig3 receives a fan of light rays 302 from diffuser 202 , and ideally all of the light rays in the fan lie on the plane of the rays 212 incident upon the diffuser . as shown , each point ( as with point p 310 ) in the scene can be illuminated by an extended source ( e . g ., along the length ( horizontal , as shown ) of the diffuser ) rather than a point source ( e . g ., from a single ray of the collimated rays ). as shown in fig4 a , with prior structured - light - based vision systems , a point p 410 can be illuminated by a thin sheet 411 of collimated light rays 412 that are aligned with a vertical axis { circumflex over ( z )} 414 . the strength of the illumination can be represented by e 0 , the irradiance that a point receives if its surface normal is aligned with { circumflex over ( z )}. if the normal at the point p is { circumflex over ( n )} 416 , its irradiance can be : e pc = e 0 ( { circumflex over ( n )}·{ circumflex over ( z )} ). as shown in fig4 b , in accordance with some embodiments , a linear diffuser 402 with scattering function d ( θ ) can be placed orthogonally to the collimated light sheet 411 such that the direction of diffusion 418 is parallel to sheet 411 . if the scattering function d ( θ ) is wide ( such as an entire semi - circle ), point p 410 can receive light from a strip 422 that spans the entire length 420 of diffuser 402 in some embodiments . as described above , the illumination incident upon the scene can be constructed of an infinite number of collimated sheets 424 with different angles of incidence on the scene in some embodiments . in the case of point p 410 , collimated sheets 424 can range in incidence angle from α 1 to α 2 . the irradiance of point p 410 due to the set of sheets 424 with incidence angles between α and α + dα , can be written as : de p = e 0 d ( α ))( { circumflex over ( n )}·{ circumflex over ( z )} ( α )) dα . let the bidirectional reflectance distribution function ( brdf ) of point p 410 be f ({ circumflex over ( n )}, { circumflex over ( v )}, ŝ ), where { circumflex over ( v )} 426 is the viewing direction determined by the location of the image sensor used to observe the scene . then , the radiance of point p 410 measured by image sensor 408 due to the above range of collimated sheets between α and α + dα can be : dl p = f ( { circumflex over ( n )},{ circumflex over ( v )}, ŝ ( α )) e 0 d ( α )( { circumflex over ( n )}· ŝ ( α )) dα . the total radiance of point p 410 due to the entire illuminating strip 422 on diffuser 402 can be found by integrating over the complete range of incidence angles from α 1 to α 2 : l p = e 0 ∫ a 1 α 2 f ( { circumflex over ( n )},{ circumflex over ( v )}, ŝ ( α )) d ( α )( { circumflex over ( n )}· ŝ ( α )) dα . because the integral depends only on the brdf , the location of point p 410 , and the normal of point p 410 , it is constant . therefore , l p can be represented as : now , consider a two - dimensional illumination pattern that can be projected onto the diffuser , such as the patterns shown in fig9 , for example . if the pattern has translational symmetry with the axis of symmetry aligned with the diffusion direction , and the brightness of the illumination sheet incident upon the diffuser strip 402 directly above point p 410 is e 0 , the radiance of point p remains unchanged . as will be apparent to one of ordinary skill in the art , alignment between an illumination pattern and a diffuser may not be exact . it should be understood that the term “ aligned ” as used herein is intended to cover perfect alignment as well as substantial , though not perfect , alignment suitable for a given implementation . when using multiple illumination patterns , we get a set of radiance measurements at each scene point ( such as point p 410 ), wherein each measurement is proportional to the brightness of illumination that the point would have received in the absence of the diffuser . the brightness of point p 410 due to the ith pattern can therefore be represented as : the factor k p , which depends on the brdf of the scene point , can reduce the brightness of specular points while maintaining the brightness of diffuse points . k p can also provide illumination to points that would have been shadowed in the case of collimated illumination ( without diffusion ). turning to fig5 a , if a scene point p 510 is diffuse ( e . g ., lambertian ), its radiance measured by an image sensor 508 can be influenced by light received from any direction . its illumination acceptance cone can therefore be the entire hemisphere 528 aligned with its normal 516 , as shown in fig5 a . in the case of a conventional structured light system , a scene point p receives a single collimated beam parallel to its vertical axis . in the case of linearly diffuse illumination , a scene point p 510 can receive illumination from all points on a strip 522 on a diffuser 502 that are visible to the point . at first glance , this may lead one to conclude that point p 510 would be brighter under diffuse illumination . however , because the energy of each light ray incident upon the diffuser would be scattered in a continuum of directions within a plane by the diffuser , the scene point would receive the aggregate of weaker illumination from a range of directions instead of a strong illumination from a single direction . if the width of the scattering function of the diffuser is chosen carefully , all diffuse points can produce approximately the same brightness under collimated illumination and diffuse illumination . the situation is , however , different in the case of specular reflection . turning to fig5 b , if point p 510 is mirror - like and is oriented such that it reflects light from an infinitesimally small patch on the light strip that is directly above it , the irradiance of point p 510 due to this patch would be significantly lower than its irradiance without the diffuser . this effect can also be seen in the case of rough specular surfaces , such as the one shown in fig5 c . the illumination directions that contribute to the radiance measured by image sensor 508 in fig5 c depend on the roughness of the surface at point p 510 . the illumination acceptance cone of point p 510 in fig5 c is narrower than the hemisphere of a diffuse point p 510 in fig5 a and broader than the delta function of a mirror - like point p 510 of fig5 b . as a specular surface gets smoother , its reflection gets brighter in the case of traditional structured light . in the diffuse illumination case , as it gets smoother , the size of the section of the light strip that it receives light from also reduces . the increase in brightness due to the increase in smoothness is offset by the decrease in brightness due to the decrease in the diffuse illumination it receives . consequently , diffuse structured light can serve to reduce the brightness of specular points while preserving the brightness of diffuse points in the scene . in some embodiments , specular reflections can be reduced by using polarized illumination and / or sensing as illustrated in fig6 . for instance , the incident light can be linearly polarized by using a polarization filter 630 in the path 632 of the illumination . because specular reflection tends to preserve the polarization of incident light while diffuse reflection does not , specularities can be reduced by using a polarization filter 634 ( with an orthogonal polarization direction to that of polarization filter 630 ) in front of an image sensor 608 used to measure radiance . in some embodiments , diffuse illumination can be used to alleviate the problem of shadows , as illustrated in fig7 a and 7 b . while points q 740 and r 742 in fig7 a are likely to be shadowed in a conventional system , these points can receive significant light in a diffuse illumination system . as illustrated in fig7 a , both points q 740 and r 742 can be illuminated by segments of the light strip on diffuser 702 . when the diffusion angle of diffuser 702 is large , each of the two points can receive light rays from an entire segment visible to it . in fact , the section of the light strip visible to a scene point does not have to continuous . it can be a set of disjoint segments , as shown in fig7 b . while a collimated light sheet corresponds to a single direction of illumination , a linearly diffuse sheet corresponds to a wide range of illumination directions that lie on the same plane . as a result , a diffuse light strip is able to project light onto surfaces that are tilted away or occluded from the original direction of light projection . fig8 a and 8 b illustrate a shadowing effect and its mitigation for the case of a sphere 802 . in the conventional case , as shown in fig8 a , only one half of sphere 802 produces light strips in an image 844 . in fact , these strips will typically be brightest at the top of the sphere and fall in brightness towards the equator of the sphere . in contrast , in the diffuse case , as shown in fig8 b , a large fraction of the bottom half of sphere 802 also produces stripes in an image 844 . in addition , the brightness of each stripe may fall more gradually , being brightest at the top and dimmest at the bottom of the sphere . points on the equator are able to receive light from a significant fraction of the light strip on the diffuser . as described above , in some embodiments , light patterns with translation symmetry can be used . examples of light patterns in accordance with some embodiments are shown in fig9 . more particularly , for example , fig9 a shows a single light stripe that can be used to scan the scene for depth estimation in some embodiments . to reduce the scanning time needed in such a system , a wide range of binary , de bruijin , and n - ary codes of the types shown in fig9 b , 9 c , and 9 d , respectively , can be used in some embodiments . these patterns can also be used for depth estimation . further reduction in the number of captured images can be achieved by using a continuous ramp brightness function pattern , a triangular brightness function pattern , and / or a sinusoidal brightness function pattern of the types shown in fig9 e , 9 f , and 9 g , respectively , in some embodiments . of these , the sinusoidal pattern in fig9 g can be used for depth estimation by phase shifting . fig9 h shows a high frequency stripe pattern that can be used in some embodiments . shifted versions of this pattern can be used to separate the direct reflection ( from the source ) and indirect reflection ( from other scene points ) components at each scene point . in some embodiments , rather than the rays of light incident upon the diffuser being collimated , the rays can be diverging from a point ( as in the case of a pinhole projector ) or converging to a point . in some embodiments , a digital projector can be used to create a light pattern . the pattern can be generated on an image plane and light rays from each point on the image plane can be projected onto the scene using a lens with a finite aperture . fig1 shows projections 1050 and 1052 of two points from a projector &# 39 ; s image plane onto a scene . projection 1052 is projected directly onto the scene and projection 1050 is projected through a linear diffuser 1002 . scene point 1056 receives all the light rays that lie within a cone of projection 1052 that the aperture of the projector lens subtends from the corresponding point of the projector &# 39 ; s image plane . a line segment 1058 in the scene ideally receives all of the light rays that are diffused from a cone of projection 1050 that the aperture of the projector lens subtends from the corresponding point of the projector &# 39 ; s image plane . the length of line segment 1058 depends on the width of the scattering function of diffuser 1002 . although the light is scattered along the direction of diffusion , it is still focused in the orthogonal direction . barring negligible high - order optical effects , the image formed by projection 1050 can be modeled as the image formed without diffuser 1002 convolved by the diffusion kernel of diffuser 1002 . this applies to points that lie within and without the depth of field of the projector . in the case of a structured - light - based vision system , if the projected pattern is i ( x , y ), the pattern that appears on the scene can be written as : where h ( x , y | d ) is the defocus kernel and d ( x , y | d ) is the diffusion kernel for the depth d of the scene point from the diffuser . for a linear diffuser , the length of the diffusion kernel ( along the direction of diffusion ) is linearly related to the depth d , but its width is zero ( or approximately zero ) and independent of height . in some embodiments , a light field can additionally or alternatively be created by placing a micro - louvre filter next to a computer display . if the micro - louvre filter has a sufficiently large aspect ratio ( e . g ., the depth of its walls is much greater than the distance between the walls ) and it is placed next to a widely scattering display ( crt , led , lcd , plasma , etc . ), then diffusion can be restricted to a single dimension . in some embodiments , a light field can additionally or alternatively be created by attaching a lenticular lens array to a widely scattering display , with the axes of translational symmetry of the illumination pattern and the lenticular array aligned with each other . in some embodiments , a light field can be created using a grooved reflector ( or linear scatterer ) as shown , for example , in fig1 . the term “ light ” as used herein is used in a general sense . the idea of linearly diffuse illumination is applicable to any form of electromagnetic radiation , including ones that lie outside the visible spectrum . although diffuser has been illustrated herein as being planar , in some embodiments , a diffuser can have any other shape . for example , in some embodiments , as shown in example 1200 of fig1 , a diffuser 1202 can be cylindrical and illumination light 1204 can be projected through the diffuser cylinder onto a scene within the cylinder and images of the scene can be captured by an image sensor 1206 from within the cylinder or from an open end of the cylinder . as shown , a cylindrical diffuser can diffuse an illumination pattern across a cross section of the diffuser &# 39 ; s cylindrical shape . as another example , in some embodiments , as shown in example 1300 of fig1 , a diffuser 1302 can be a radial diffuser and an illumination pattern 1304 with radial symmetry that is aligned with the radial diffuser can project light through the diffuser onto a scene . images of the scene can then be capture by an image sensor 1036 . in accordance with some embodiments , as shown in fig1 , any suitable computing device ( s ) 1102 can be provided for controlling a light pattern ( e . g ., such as shown in fig9 ) provided by a source of linear diffused light 1104 as described herein , for processing images and / or video detected by an image sensor 1108 as described herein , and / or for performing any other suitable functions . more particularly , for example , each of any such computing device ( s ) can be any of a general purpose device such as a computer or a special purpose device such as a client , a server , etc . any of these general or special purpose devices can include any suitable components such as a hardware processor ( which can be a microprocessor , digital signal processor , a controller , etc . ), memory , communication interfaces , display controllers , input devices , etc . in some embodiments , any suitable computer readable media can be used for storing instructions for performing the processes described herein . for example , in some embodiments , computer readable media can be transitory or non - transitory . for example , non - transitory computer readable media can include media such as magnetic media ( such as hard disks , floppy disks , etc . ), optical media ( such as compact discs , digital video discs , blu - ray discs , etc . ), semiconductor media ( such as flash memory , electrically programmable read only memory ( eprom ), electrically erasable programmable read only memory ( eeprom ), etc . ), any suitable media that is not fleeting or devoid of any semblance of permanence during transmission , and / or any suitable tangible media . as another example , transitory computer readable media can include signals on networks , in wires , conductors , optical fibers , circuits , any suitable media that is fleeting and devoid of any semblance of permanence during transmission , and / or any suitable intangible media . although the invention has been described and illustrated in the foregoing illustrative embodiments , it is understood that the present disclosure has been made only by way of example , and that numerous changes in the details of implementation of the invention can be made without departing from the spirit and scope of the invention , which is limited only by the claims that follow . features of the disclosed embodiments can be combined and rearranged in various ways .