可持久化數據結構加掃描線

Traditional cameras and image sensors can only obtain two-dimensional images, lacking depth information, which imposes great limitations on the perception and understanding of real objects. In recent decades, with the continuous development of high-definition, high-speed image sensors and computing capabilities, three-dimensional surface imaging technology has achieved remarkable results in research, engineering, and business. In particular, the structured light three-dimensional surface imaging technology has been applied to various places.

傳統的相機和圖像傳感器只能獲取缺乏深度信息的二維圖像，這對真實物體的感知和理解施加了很大的限制。 近幾十年來，隨著高清，高速圖像傳感器和計算功能的不斷發展，三維表面成像技術在研究，工程和商業方面取得了顯著成果。 特別地，結構化光三維表面成像技術已被應用于各個地方。

For every major visual effects movie, the principal actors’ bodies and heads are scanned before or during production using the types of scanners. The resulting 3D scans are used to build digital stunt doubles for actors, to aid in creating realistic aging transformations, or to provide a starting point for morphing into a computer-generated creature.

對于每部主要視覺效果電影，在制作之前或制作過程中，都使用掃描儀類型對主要演員的身體和頭部進行掃描。 由此產生的3D掃描用于為演員建立數字特技雙打，以幫助實現逼真的衰老轉換，或提供變身為計算機生成生物的起點。

Projecting a narrow band of light across three dimensions in the shape of a surface produces a line of illumination that appears distorted from perspectives other than that of the projector and can be used for an exact geometric reconstruction of the surface shape.

在表面形狀的三個維度上投射一條狹窄的光帶會產生一條照明線，該照明線從投影機以外的其他角度看起來會變形，并且可以用于表面形狀的精確幾何重構。

A faster and more versatile method is the projection of patterns consisting of many stripes at once, or of arbitrary fringes.A sinusoidal fringe is generated by computer programming, and the sinusoidal fringe is projected to the object to be measured through a projection device. The camera is used to capture the degree of curvature of the fringe modulated by the object, the pattern appears geometrically distorted due to the surface shape of the object.

更快，更通用的方法是一次投影由多個條紋組成的圖案或任意條紋。通過計算機編程生成正弦條紋，然后將正弦條紋通過投影設備投影到要測量的對象上。 相機用于捕獲物體調制的條紋的曲率程度，圖案由于物體的表面形狀而出現幾何失真。

This article mainly describes the principle and implementation of the three-dimensional surface imaging technology of light-composition, especially the phase measuring profilometry (PMP).

本文主要介紹了光組成三維表面成像技術的原理和實現，尤其是相位測量輪廓圖(PMP)。

Compared with encoding structured light methods such as Binary code and Gray code, PMP does not require complex encoding, and the algorithm can calculate the height value according to the information of each pixel, so as to achieve full-scale high-precision measurement. In the phase method, the following steps are usually included :

與二進制碼，格雷碼等編碼結構光方法相比，PMP不需要復雜的編碼，該算法可以根據每個像素的信息計算出高度值，從而實現了全方位的高精度測量。 在階段方法中，通常包括以下步驟：

Project a structured texture image (usually a sinusoidal grating pattern) onto the surface of the object to be measured.

將結構化的紋理圖像(通常是正弦光柵圖案)投影到要測量的對象的表面上。

Record raster images phase-modulated by the height of the object.

記錄通過對象高度進行相位調制的光柵圖像。

Use grating analysis technology to extract the phase.

使用光柵分析技術提取相位。

Use a suitable phase unwrapping algorithm to obtain a continuous phase distribution that changes in proportion to the height of the object.

使用合適的相位展開算法來獲得連續的相位分布，該分布與對象的高度成比例地變化。

The calibration system maps the expanded phase distribution to the real-world three-dimensional coordinate system.

校準系統將擴展的相位分布映射到實際的三維坐標系。

正弦波模式的產生 (Generation of Sinusoidal Pattern)

Phase measurement profilometry needs to project sinusoidal grating patterns with different phases onto the surface of the object.

相位測量輪廓儀需要將具有不同相位的正弦光柵圖案投影到物體表面。

The LCD projector can use a personal computer to control the projected image. The sinusoidal grating image is generated by projection software, which provides an efficient structured light projection scheme. We assume that the resolution of the LCD projector is R x C. For each column c in the generated sinusoidal grating image, c=0,1,2,…,C-1, there are:

LCD投影儀可以使用個人計算機控制投影圖像。 正弦光柵圖像由投影軟件生成，該投影軟件提供了有效的結構化光投影方案。 我們假設LCD投影儀的分辨率為R xC。對于生成的正弦光柵圖像中的每一列c， c = 0,1,2，…，C-1 ，有：

F_{n}(r,c) is the pixel value at (r,c) in the raster image after phase shifting k steps. In our example, k={1,2,3 ,4}, p is the grating period in pixels, δ is the phase shift increment.Figure below shows the sinusoidal raster images generated by the software.

F_ {n}(r，c)是相移k步后光柵圖像中(r，c)處的像素值。 在我們的示例中，k = {1,2,3，4}，p是以像素為單位的光柵周期， δ是相移增量。下圖顯示了該軟件生成的正弦光柵圖像。

Each image is shifted by a quarter of a period to the right from the previous image. Image By Author每個圖像從上一個圖像向右移動四分之一周期。 圖片作者

相位測量輪廓儀 (Phase Measuring Profilometry)

The sinusoidal grating image generated by the projection module is projected onto the surface of the object placed on the reference plane, and the refracted light is captured by the image acquisition module (Camera).

由投影模塊生成的正弦光柵圖像被投影到放置在參考平面上的對象的表面上，并且折射光被圖像獲取模塊(相機)捕獲。

The following figure shows the picture when 4 sine grating images with different phases are projected onto the surface of the object using the phase shift method when k=4..Image By Author下圖顯示了當k = 4時使用相移方法將4個不同相位的正弦光柵圖像投影到對象表面時的圖片。

Since the projected sinogram changes in the same pattern in the column direction, the contour of the object can be constructed by the calculation results of each row.

由于投影的正弦圖在列方向上以相同的模式變化，因此可以通過每行的計算結果來構造對象的輪廓。

Source資源

We assume that point O is the intersection of the optical axis and the reference plane, point O is used as the origin of the coordinate and the phase is 0.

我們假設點O是光軸與參考平面的交點，點O被用作坐標的原點，并且相位為0。

The period of the sine grating image projected on the reference plane is p_{o}, the period of the original sine grating image is

投影在參考平面上的正弦光柵圖像的周期為p_ {o} ，原始正弦光柵圖像的周期為

The sensor in the camera receives the light reflected at point D on the surface of the object, if there is no object, the same position in the sensor will receive the light reflected at point C on the reference plane. Correspondingly, the light refracted at point D on the surface of the object is the same as the light refracted at point G on the horizontal plane without an object. So the phase of the projected image at point D is equal to the phase at point G, and there are:

相機中的傳感器接收在物體表面D點反射的光，如果沒有物體，則傳感器中相同的位置將接收在參考平面上C點反射的光。 相應地，在物體表面上的點D處折射的光與在沒有物體的情況下在水平面上的點G處折射的光相同。 因此，投影圖像在D點的相位等于G點的相位，并且有：

Where,

哪里，

Is the phase value of the projected image at point C.

是投影圖像在C點的相位值。

The phase difference between point D and point C is:

D點和C點之間的相位差為：

According to the geometric relationship, we get:

根據幾何關系，我們得到：

According to the above formula , we get:

根據以上公式，我們得到：

OD is the height of the object at point O.

OD是對象在點O處的高度。

The general formula is:

通用公式為：

Where,?o(x,y) is the phase at the point (x,y), and ?r(x,y) is the phase on the reference plane at the corresponding point.

其中，φO(X，Y)是在該點的相(X，Y)，以及φR(X，y)是在相應點上的基準平面的相位。

相移輪廓儀 (Phase Shift Profilometry)

When the light is stable and the Camera is linear, the light intensity I(x,y) at a certain point (x,y) in the captured image can be expressed as the following formula :

當光線穩定且相機呈線性時，可以將捕獲圖像中某個點(x，y)的光強度I(x，y)表示為以下公式：

Where,B(x,y) is the background light intensity, C(x,y) is the amplitude value of the sinusoidal grating, and ?(x,y) is the phase value modulated by the height of the object.

其中，B(x，y)是背景光強度，C(x，y)是正弦光柵的幅度值， ? (x，y)是由物體高度調制的相位值。

I(x,y) can be obtained by camera. In order to eliminate the B(x,y) and C(x,y) in the formula and get ?(x,y), we use aphase extraction algorithm called the phase shift method.

I(x，y)可以通過相機獲得。 為了消除公式中的B(x，y)和C(x，y)并獲得? (x，y)，我們使用一種稱為相移法的無相提取算法。

In the phase shift method, the phase will be moved k times, each time the same value is θ_{k}. The formula \ref{eq:2.6} can be written as:

在相移方法中，每次相同的值是θ_ {k}時，相位將移動k次。 公式\ ref {eq：2.6}可以寫成：

Let,

讓，

Substitute in the above formula, we can get:

用上面的公式代替，我們可以得到：

And,

和，

So we get the phase value:

這樣我們就得到了相位值：

Then the surface height of the object can be calculated

然后可以計算出物體的表面高度

The phase shift method uses the light intensity information of multiple images to calculate the phase of each point, so it has a certain anti-noise ability. But in the sampling process, the object is required to remain still, so it is not suitable for dynamic measurement.

相移法利用多個圖像的光強度信息來計算每個點的相位，因此具有一定的抗噪能力。 但是在采樣過程中，要求對象保持靜止，因此不適合動態測量。

相位展開 (Phase Unwrapping)

At this time, the final continuous phase is not what we want, because the phase obtained by the phase shift technique is an inverse tangent function, so the original phase will be compressed in between [-π/2,π/2] with a period of π .

此時，最終的連續相位不是我們想要的，因為通過相移技術獲得的相位是反正切函數，因此原始相位將在[-π/ 2，π/ 2]之間壓縮為π的周期。

Thus there will appear repeatedly π gap wrapped phase map, and the removal of these drops it is called phase unwrapping technique.

因此，將反復出現π間隙包裹的相位圖，將這些液滴的去除稱為相位展開技術。

According to Shannon’s sampling theorem, in the correct two-dimensional phase distribution, the absolute value of the phase difference between each point and any point adjacent to it must be less than π to avoid aliasing. Therefore, when the phase difference between the reference point and its neighboring point is greater than π, phase unwrapping is required, and a value of ±2π needs to be added so that a continuous phase distribution can be obtained. This is the basic theory of phase unwrapping.

根據香農的采樣定理，在正確的二維相位分布中，每個點和與其相鄰的任何點之間的相位差的絕對值必須小于π以避免混疊。 因此，當參考點與其相鄰點之間的相位差大于π時，需要相位解纏，并且需要加上±2π的值，以便可以獲得連續的相位分布。 這是相位展開的基本理論。

(a) One-dimensional phase distribution diagram, the phase value will be limited to 2π modulus. (b) After judging, add an integer multiple of the period 2π at each phase jump to obtain a continuously distributed phase map.(a)一維相位分布圖，相位值將限制為2π模數。 (b)判斷后，在每個相位跳變處添加周期2π的整數倍，以獲得連續分布的相位圖。

Generally, a two-dimensional phase expansion method can be expressed as the following formula:

通常，二維相擴展方法可以表示為以下公式：

Where, ? represents the phase value after expansion, ?(x,y) represents the phase value in the original 2π modulus,?_0 represents the phase value of the reference neighboring point, and Round[x] represents the integer value closest to x.

其中， ?表示擴展后的相位值， ?(x，y)表示原始2π模量的相位值， ? _0表示參考相鄰點的相位值，Round [x]表示最接近x的整數值。

This basic rule is only applicable to phase diagrams with small noise and no inconsistency. Once the noise increases or there is discontinuity in the phase itself , resulting in discontinuities.

該基本規則僅適用于噪聲小且沒有不一致的相位圖。 一旦噪聲增加或相位本身不連續，就會導致不連續。

結論 (Conclusion)

This lesson covers the basic, low-level operations and tools of image processing, which are necessary for understanding most of the commonly used methods and tools of computer vision

本課程涵蓋了圖像處理的基本，低級操作和工具，這對于理解計算機視覺的大多數常用方法和工具是必不可少的

翻譯自: https://towardsdatascience.com/structured-light-scanning-c125d5e06c41

可持久化數據結構加掃描線

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