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Obtaining Focused Images Using a Non-Frontal Imaging Camera*

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Obtaining Focused Images Using a Non-Frontal Imaging Camera* A*a4z Is-tlersta^/i( LJarK-s Lop, t444 Obtaining Focused Images Using a Non-frontal Imaging Camera* Arun Krishnan and Narendra Ahuja BeckmanInstitute, Universityof Illinois 405 North MathewsAve., Urbana IL 61801,U.S.A. e-mai1:[email protected], e-mai1: [email protected] Abstract , three arbitrary points simultaneously. If the scene points of interesi number more than This paper is concerned wiih obtaining focused im- three, or if the points are spread out in a wide ages of a scene using a non-frontal camera. The scene, the rota- lion of the sensorplane about the optic non-frontal camera used here has a sensor surface center,or camera panning, is exploited which is desoibed which is planar, can be dynamically translated and in Section 3. The focusing ability of the non-frontal oriented, and can be rotated with respect io the op- camera.in this case derives from the fact that when iic center. Up to three object points in a scenecan the non-frontal camera 1(a) panned be focused simulaneously using the translation and is about the lens centel, a fixed scene point orienta,tion degrees of lreedom of the sensor plane. is imaged in succes- sive frames angles) with different values A scene of arbitrary size and depth can be focused {pan of u. There will be one such value of u, and using the rotational degree of freedom to obtain a equivalently, one such image frame, for which the poini panoramic image, showing up io 360 degree view scene is imaged at the sharpest focus. ofthe scene- The focusing ability directly leads to This value of r: is achieved through (manual range estimates. The range and focused intensities or motorized) mechani- cal adjustments inltandard cameras, car be combined to generate 3D stereo displays of for one object rne scene. ai a time. Analysis of the image sequence gener- ated by a non-frontal camera panning about its lens 1 fntroduction center can therefore yield a composite focused im- age for objects at all depths in an arbitrarily wide This paper describes methods for obta.ining focused scene. A panoramic focused image of up to 360 de- images of scenes of arbitrary size and depth using gree view of a scene can be obtained by selecting a new type of camera introduced in [5] called non- the corresponding bounds for pan angles. Section 4 frontal imaging camera. Such cameras have sensor discussescombining the focused intensity estimates surfaces which can be dynamically configured with with the range estimates derived from the focusing respect to the optic center, with multiple degrees process to synthesize a stereo display of the scene of freedom. For example, the non-frontal camera from the monocula;r image sequenceacquired by a desoibed in [5] has one trauslational degree and single panning non-frontal camera. one rotational degree of freedom. In this paper we-are concerned with the use of 2 Focused Single FYame Images. the non-frontal camera of Figure 1(a) to obtain focused images. Standard cameras only have one This section desoibes methods for obtainine a fo- focus adjustment which effectively cha.nges the fo- cusedimage ofobjects visible in a singleview using cus distance (o) between the lens and tle sensor a non-frontal camera. The sensor surface's capabil- plane. Further, in standard camerae all points on ity for dynamic reorientation is used for this pur- the sensor plane have the same o value. In con- pose. A standard camera can only simultaneously trasi, non-frontal cameras have o values that vary focus on scenepoints that are all at the same range across the sensor surface. This property of non- from the camera or that all lie within the depth of fronta,l cameras is used in Section 2 to focus uD to field. With the non-frontal camera. uo to three *The support of the Advanced Research Projects Agency points (objects), not all wit hin the deptli of field o{ under grant N00014-93-1-1167 is gratelully acknowledged. the standard camera, can be imaged in sharp focus. One Point: In this eimple case, the fixed distance tate about the optic center, the panning motion to the object point determines the sensor plane dis- sufficesro focus each scen" point a. d""ciib"d be tance o. For standard as well as non-frontal cam- low. eras, the desired value of o could be obtained by translating the sensor plane- A non-frontal camera 3 Obtaining Focused Images by also has the option of using a sensor surface tilt Panning a control to achieve the desired o value. Non-frontal Camera Two Points: Standard cameras cannor tmage two Consider a non-frontal camera with a sensor plane or more scene points that are not all at the same that is not perpendicularr,o the optical axis. Tbis range (within the depth of field). Two scenepoints causes different sensor pixels to be at difierent dis- specify two points behind the lens that the sensor tances from the lens. The non-frontal camera will plane should pass through. With position control image with sharp focus a volume of object space . and tilt control, the sensor plane can be positioned that is also tilted with respect to the optical axis. pass to through any two arbitrary points (within So in any one image frame, there will be scene the motion lirnits of the stages), and thus to image poiats in sharp focus that are at difrerent depths the two points in focus. from tbe camera. If tbe entire cam"ra i. now .o- Three Points; Tilt control about two orthosona,l tated in small steps about a vertical axis throush axes along with posirion cootcol allows the sensor t he lenscent€r, then the entire scenewill be sequen- plane to achieve arbitrary position and orientation tially imaged by a plurality of fiames. By choosing inside the camera. Three scene pohts define three tbe angleof rotation betweensuccessive frames to fixed points behind the lens that the sensor plane be suficiently small, each scene point will be im- must pass through. Therefore by maximizing the aged in multiple frames, but by different sensor el- shatpness at each point, the camera can sharply ements (at difierent locatious on the sensor plane) focus three arbitrary pohts simultaneously. iq different frames. Since [he sensorelements are Four or more Poirrts: Ima,ging more than three located at difierent distances from the lens center, scene points in sharp focus simultaneously would the scene poiut will therefore be imaged with dif- require warping the sensor plane and is difficult ferent levels of blur, the sharpest focus image oc- at this time. Alternatively, one could maximize curring for some rotation angle, and progressively the sha,rpnessof all points combined. This may be blurred images as the camera rotates further away. achievedby controlling the position and orientation To determine wher: a scene point has been imaged of the sensor plane such that a chosen function of with sharp focus, standard focus criterion functions the image blurs at the image points is minimized. that esiimate the high frequency content can be In conjunction with a model of the imase blur a.s used[3, 8, 12,9]. a function of the displacementof rbe senlor plane Along with the focused image, ihe u value coue- with respect to the true image location, the sen- sponding to the focused image of a scene point sor plane can be configured to minimize the mean also yields its range from the camera, using the squared distance from the true image locations of lens law as done in the range from focus meth- the points. ods110, 1, 2, 61. A solution that does not require warping the sen- Before we give the algorithm, two factors must be sor plane and thai also does not compromise on the discussedthat distinguish the images obtained from focused image quality is to reconstruct the focused those obtained using the standard camera. First, image from a series of images that have individual the variation in the registered brightness of the scene points in sharp focus, A series of images, same scene point from different directions (pan an- each taken with difierent sensor plane positions gles) must be taken into account (due to varying (different values of o), can be analyzed io deier- distance between sensor plane points and lens cen- mine sharply focused regions, a.ndthen the focused ter). Second, the varying degrees of perspective regions from each image can be combined to obtain warping at different locations on the non-frontal a composite focused image of the scene 111,4]. sensor plane must be considered If a standard camera with a frontal, translating Irradiance dependency on tilt angle: The sensor plane is used, objects in difierent scene di- pixel brightness (,4) in standard frontal cameras rections will have to be focused by (mechanically) depends on the area of the lens aperture (A1",,), translating the sensorptane. Using a non-frontal the scene radiance (-L), the mea,ndistance between camera in which the sensor plane is allowed to ro- ihe lens and the sensor plane (.\) and the plxel lci- caiion (z, gr) as shown below Algorithm: Let j:Q. d=0. InitializeC and \2 then execute the following steps_ L=Atensxr,;=_-__ tLr'+Y'+^212 . Capture the jlh image Ii. o Compensate for the intensity variation due to It can be shown that for the non-frontal camera sensor plane tilt and position on the sensol plane with sensorplane tilt of o, the expressionfor pixel usiag Equation 1. brightnessbecomes: o Dewarp ihe intensity rectified image using Equa- tions 2 and 3.
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