以取像系統參數的物體形狀估測法之研究

摘要本文研究有效率及準確的物體形狀量測法, 這種從2-D影像中延伸出3-D形狀的方法, 此法簡稱為形狀估測法(shape from X). 形狀估測法包括: 表面紋理法(shape from texture), 立體量測法(shape from stereopsis), 對焦/失焦法(shape from focus/defocus), 影像移動法(shape from motion), 距離感測器(shape from range sensor), 及影像強度法(shape from intensity)等. 在形狀估測過程中, 我們常遇到的問題. 如陰影, 凹凸面, 物體邊界及不連續面等. 沒有一種形狀估測法可以解決上述的所有問題, 因為每個方法皆有其限制及其優劣點. 故吾人將整合其中一些方法發展出有效率及準確的形狀估測法. 首先, 吾人從相機模型(camera model), 表面幾何模型(surface geometry model)及表面反射模型(surface reflectance model)建立起取像系統參數(imaging system parameters), 包括: 光學參數—焦距 f 及光圈 F, 相機參數— k , 模糊參數—σ 及表面參數—表面法向量(nx ,ny ,nz ), 表面梯度(p, q), 傾斜(slant)角, 偏斜(tilt)角..等. 然後, 我們應用三種方法—主動式立體幾何法(active stereopsis), 失焦法及光度濃淡法(shape from shading)來完成形狀估測. 雖然以幾何像差(geometric disparity)為基礎被動式立體幾何法(passive stereopsis)簡單快速, 但對光滑及均勻表面紋路無法發揮功效, 因此我們用雷射光束(laser beam)為光源來發展主動式立體幾何法以量測物體的外形. 失焦法沒有對映(corresponding)及匹配(matching)等問題. 故我們利用高斯模糊函數(Gaussian blurred function)來分析失焦的影像求得物體的深度. 因為高斯模糊函數的sigma值會隨著取像條件的不同而改變, 所以如果能精確的量出sigma值就能推導出物體與相機的距離, 我們進一步使用一種近似法—根基函數網路法(the radial basis function networks, R.B.F.N)—來逼近sigma值. R.B.F.N 是利用調整三層類神經網路的高斯函數的位置及大小來逼近失焦影像中的模糊情況. 一個平滑且不透明物體經光源照射後, 在影像上會產生濃淡明暗度的變化, 我們利用此光度濃淡法來重建物體的外形, 光度濃淡法是以照度方程式(irradiant equation)為基礎, 照度方程式包括: 反射圖(reflectance map)及反射參數(reflectivity parameters)—反照率(albedo)及入射亮度(incident radiance). 當遠光源照射時, 被照射物體的表面反射參數可視為常數, 但近光源照射時, 被照射物體的表面反射參數則非常數. 我們發展出遮罩式光度立體法(masked photometry stereo)來作多光源所產生的光度立體影像中以背景圖為遮罩處理的物體形狀重建法. 被遮罩處理後的光度立體影像的Lambertian反射圖將被代入反射函數中以求得物體表面梯度, 我們使用了反射函數的線性近似法且以分離式近似及有限差分, 用深度(depth, Z(x, y))參數取代表面梯度將反射函數線性化. 本文整合了系統影像參數到形狀估測法中, 以研究出區域及可平行處理的影像重建法. 這些方法及理論為了確保其準確性, 我們將理論代入合成影像(synthetic images)中, 主動式立體幾何法以加工後的工件經三次元量床量測物體表面所得的曲面資料, 建立成合成影像, 失焦法以高斯函數來模擬物體邊界在失焦時的影像, 光度濃淡法則以電腦繪圖建立物體形狀, 並且以程式模擬光源大小, 方向及反射函數來建立合成影像, 驗證理論無誤後, 再代入實際的影像進行實驗, 吾人獲得滿意的結果, 故此參數式的方法是有效及準確的物體外形量測法. 本文共分為五章, 第一章為簡介, 包括研究動機, 形狀估測技術的文獻回顧, 及研究目的. 第二章為形狀重建技術, 在問題的描述中, 將形狀估測技術分成主動式及被動式, 對各種方法加以探討, 接著討論空間及頻率域, 區域及廣域, 單像機及雙像機等方法, 並且對形狀重建的名詞加以闡述及說明, 然後對整個取像系統歸納出與形狀重建相關的影像參數, 且將本文所提的三種方法—主動式立體幾何法(active stereopsis), 失焦法(shape from defocus)及光度濃淡法(shape from shading)詳細的介紹及理論說明. 第三章為實驗的取像架構, 分成主動式立體幾何法, 失焦法及光度濃淡法等部分. 第四章為實驗的結果與討論, 包括形狀重建, 深度計算, 誤差分析, 及運算時間等. 第五章結論及未來的研究.

關鍵字

形狀估測法；主動式立體幾何法；失焦法；光度濃淡法；遮罩式光度立體法

並列摘要

Abstract There is a multitude of methods for deriving a three-dimensional shape from its two-dimensional images, which are known as shape from X. In this paper, we have attempted to develop an efficient and accurate parametric estimation for shape recovery. The techniques of shape from X include the shape from texture, the shape from stereopsis, the shape from focus/defocus, the shape from motion, the shape from range sensor, and the shape from intensity. During the shape recovery procedures, we have met many troublesome problems, such as shadow areas, convex/concave ambiguity, object boundaries and discontinuous surface. None of the methods mentioned above can solve all the problems for shape reconstruction, as every method has its limitations and constraints during applications. First, we use the camera model, the surface geometry model, and the surface reflectance model to form imaging system parameters including optical parameters “focal length f and aperture F”, “camera parameter k”, “blur parameter σ”, and surface parameters such as “surface normal (nx ,ny ,nz )”, “surface gradient (p, q)”, “surface slant (ψ)”, and “surface tilt (θ)”. Second, we use three major methods – active stereopsis, shape/depth from defocus and shape from shading – to finish shape recovery. Although passive stereopsis based on the geometric disparity is a simple and fast method, it works improperly on smooth and uniform surfaces, and has corresponding and matching problems. Therefore, we use the active stereopsis with a laser beam to measure the profile of the surface from object to camera. Shape/depth from defocus doesn’t have the image-to-image problems of matching and occlusion. We use the shape/depth from defocus method to analyze the defocused images to obtain depth information using the Gaussian blurred function. Since the sigma value of the Gaussian function depicts on the intensity of images grabbed by imaging devices, we needed an approximate method, the radial basis function networks (R.B.F.N), to approach the sigma value directly in the spatial domain. The “R.B.F.N” regularizes the center position and the sigma value of the Gaussian function based on the radial basis function to fit the profile of the defocused image by three layers of neural networks. As a smooth opaque object will give rise to a shade image, we apply the shape from shading to recover the shape. The shape from shading is based on the irradiant equation which is formed by reflectance map and reflectivity parameters, like albedo and incident radiance. Under a near light source, the reflectivity parameters will vary on the illuminated surface. We propose a method, called masked photometry stereo, which applies the background images as masks onto photometry stereo images under multi-light sources. The masked photometry stereo images’ Lambertian reflectance map will be taken into the reflectance function in order to obtain the surface gradients. Then, we incorporate a linear approximation of the reflectance function and also use discrete approximations and finite differences to linearize the reflectance function in depth “Z (x, y)”, instead of surface gradients p and q. We have integrated the image parameters into shape from X in order to obtain a local and parallel computation for shape recovery. The algorithms have been tested on synthetic and real images, and have obtained satisfactory results.

並列關鍵字

masked photometry stereo ； shape from X ； active stereopsis ； shape from defocus ； shape from shading

參考文獻

1. D. Marr, Vision: A Computational Investigation into the Human Representation and Processing of Visual Information, W. H. Freeman and Company, New York, 1982.

2. G. Ramanourthy, R. V. Shankar and M. Suk, Pose Determination Using Vertex-Pairs on the Connection Machines, Tools for Artificial Intelligence, 512-517, 1989.

4. R. Massen, Multi-sensorial Cameras in Industrial Quality Inspection, Advanced Technologies, Intelligent Vision, 23-26, 1995.

6. R. Jain, R. Kasturi and B. G. Schunch, Machine Vision, McGraw-Hill, New York, 1995.

7. J. J. Gibson, The Perception of the Visual World, Houghton Mifflin, Boston, 1950.

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以取像系統參數的物體形狀估測法之研究

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