APPARATUS AND METHOD FOR QUANTIFYING THE SURFACE FLATNESS OF THREE-DIMENSIONAL POINT CLOUD DATA

Abstract

A method that quantifies the surface flatness of 3D point cloud data in which a test statistic is proposed to indicate the surface flatness based on the threshold of the allowed bump level, the confidence level of test statistics and data density. The method comprises steps of converting the LIDAR measured points to coordinates along the axes using the principal component analysis (PCA) technique; calculating a Z.sub.α value based on the coordinates and predetermined bump tolerance: comparing the Z.sub.α value with a Z score of a test statistic to perform a null hypothesis; and rejecting the null hypothesis when the Z.sub.α value is greater than the Z score.

Claims

1. A method for quantifying the surface flatness of LIDAR three-dimensional (3D) point cloud data, comprising: generating a laser light beam from a laser; scanning the laser light beam using a scanner along a three-dimensional (3D) target surface; detecting a point cloud of reflected light from the target surface with a photodetector; converting the point cloud to coordinates along coordinate axes according to the attributes of the target surface with a principal component analysis (PCA) technique in a controller; calculating a Z.sub.α value based on the coordinates and a predetermined bump tolerance, wherein the Z.sub.α value has the following relation: $Z_{\alpha }=\frac{\left|{\stackrel{\_}{r}}_{\mathrm{local}}-{\stackrel{\_}{r}}_{\mathrm{global}}\right|-d}{{\sigma }_{r,\mathrm{global}}/\sqrt{N_{\mathrm{local}}}};$ wherein r.sub.local is a local mean of coordinates, r.sub.global is a global mean of coordinates, σ.sub.r,global is a global standard deviation of coordinates, N.sub.local is a number of local sample events, and d is a predetermined bump tolerance; comparing the Z.sub.α value with a Z score of a test statistic to perform a null hypothesis, wherein the Z score is a value that corresponds to a confidence level; and rejecting the null hypothesis when the Z.sub.α value is greater than the Z score; producing three-dimensional measurements of the target surface based on the Z.sub.α value, thereby quantifying surface flatness of the target surface.

2. The method as claimed in claim 1, wherein the predetermined bump tolerance is in a range of 0.5 to 1.5 centimeters.

3. The method as claimed in claim 1, wherein the attributes of the target are length, width and thickness of the target surface.

4. The method as claimed in claim 1, wherein the test statistic is determined by a null hypothesis of a one tail test that states that surface flatness of the target surface is smaller than a predetermined bump tolerance.

5. The method as claimed in claim 1, wherein a target with a known bump size is used to determine the predetermined bump tolerance, d.

6. The method as claimed in claim 1 wherein the scanner is selected from a mirror, a polygonal mirror, or a MEMS device.

7. An apparatus for implementing the method of claim 1 including a laser, a scanner, a photodetector, and a controller.

8. The method as claimed in claim 1, further comprising performing one or more calibrations for one or more target surfaces with different incident angles, ranges, texture and refractivity to correct detection distortion.

9. The method as claimed in claim 1 wherein the photodetector is selected from a silicon avalanche photodiode, a photomultiplier, a charge-couple device (CCD), or a complementary metal-oxide-semiconductor (CMOS) device.

10. The apparatus of claim 7, wherein the controller is one or more microprocessors.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0012] The invention is presented in more details using implementation examples of the drawings below. In the attached drawings:

[0013] FIG. 1 depicts a LIDAR system for quantifying surface flatness according to one aspect;

[0014] FIG. 2 is a flow chart illustrating a method that quantifies the surface flatness of 3D point cloud data in accordance with an embodiment of the present invention;

[0015] FIG. 3 is an exemplary diagram illustrating a flatness of a ceiling line where the wall meets the ceiling;

[0016] FIG. 4 is an exemplary diagram illustrating a Null hypothesis of a one tail (right) test with a bell-shaped curve;

[0017] FIG. 5 is an exemplary diagram illustrating a LIDAR system being disposed to collect data points that represents a three-dimensional shape in a room;

[0018] FIGS. 6A-6C are exemplary diagrams illustrating the conversion of the LIDAR points return to coordinates along the coordinate axes;

[0019] FIGS. 7A and 7B are two-dimensional (2D) plot diagrams illustrating the distributions of the values by performing the method to the coordinates of FIG. 6A in accordance with an embodiment of the invention;

[0020] FIGS. 8A and 8B are 2D plot diagrams illustrating the distributions of the values by performing the method to the coordinates of FIG. 6B in accordance with an embodiment of the invention; and

[0021] FIGS. 9A and 9B are 2D plot diagrams illustrating the distributions of the values by performing the method to the coordinates of FIG. 6C in accordance with an embodiment of the invention.

DETAILED DESCRIPTION

[0022] In the following description, the apparatuses and methods for quantifying the surface flatness of three-dimensional (3D) point cloud data and the likes are set forth as preferred examples. It will be apparent to those skilled in the art that modifications, including additions and/or substitutions may be made without departing from the scope and spirit of the invention. Specific details may be omitted, so as not to obscure the invention; however, the disclosure is written to enable one skilled in the art to practice the teachings herein without undue experimentation.

[0023] Turning to FIG. 1, a LIDAR system 10 that can quantify surface flatness is depicted. The LIDAR system 10 includes a laser source 20 which emits light 60, the light 60 typically passing though optics 30 such as a collimating lens. The laser 20 may be, for example, a 600-1000 nm laser, or a 1550 nm band laser. A single laser source or multiple laser sources may be used. Alternatively, a flash LIDAR camera may be employed.

[0024] The light 60 is incident on a scanning device 90. The scanning device may be a rotating mirror (polygonal or planar), a MEMS device, a prism, or another other type of device that can scan a laser beam on the surface of a target object 100 to be scanned. Image development speed is controlled by the speed at which the target object is to be scanned. The scanner beam 65 is reflected as reflected beam 75 which is directed off the scanning device 90 into beam 70 through optics 40 and into photodetector 80. Photodetector 80 may be selected from solid-state photodetectors such as silicon avalanche photodiodes or photomultipliers, CCDs, CMOS devices etc. A controller 50 electrically communicates with laser source 20, photodiode 80, and scanning device 90. The controller may be one or more processing devices such as one or more microprocessors, and the techniques of the present invention may be implemented in hardware software, or application-specific integrated circuitry.

[0025] The LIDAR system 10 generates a point cloud of data. A point cloud is a collection of data points that represents a three-dimensional shape or feature. Each point in the point cloud is associated with a color, which indicates the intensity of the received signal. For measuring applications, a 3-D model from the point cloud is generated from which measurements may be taken.

[0026] With reference to FIGS. 2 and 3, FIG. 2 is a flow chart illustrating a method that quantifies the surface flatness of 3D point cloud data in accordance with an embodiment of the present invention; and FIG. 3 is an exemplary diagram illustrating the flatness of a ceiling line where the wall meets the ceiling.

[0027] As shown in FIG. 2, in this embodiment, the method using aforementioned LIDAR system to quantify the surface flatness of a scanned object using 3D point cloud data, which comprises steps of S100: obtaining LIDAR measured points from target 100, S110: converting the LIDAR measured points to coordinates along the coordinate axes according to the attributes of the target 100, S120 calculating a Z.sub.α value based on the coordinates and predetermined bump tolerance, S130 comparing the Z.sub.α value with a Z score of a test statistic to perform a null hypothesis, and S140 rejecting the null hypothesis when the Z.sub.α value is greater than the Z score.

[0028] In the step of S110, a principal component analysis (PCA) is performed to transform the attributes of the target 100 into coordinate axes. PCA is a dimensionality-reduction method that is used to reduce the dimensionality of large data sets.

[0029] The target can include, a local bump/projection on the surface of a target. For example, the target may be a relatively flat surface such as a wall, a ceiling or a floor or a join of two surface such as a ceiling line shown in FIG. 3.

[0030] With further reference to FIG. 4, FIG. 4 is an exemplary diagram illustrating a Null hypothesis of a one tail (right) test with a bell-shaped curve. In the steps of S120 to S140, the present invention proposes a Null hypothesis of a one tail (right) test that claims the surface flatness of the target is smaller than a predetermined bump tolerance (i.e., considered as flat). The value of the Z score corresponds to the standard normal distribution table. For example, the Z score is 1.645 when the confidence level is 95%. In another embodiment, the Z score is 2.363 when the test statistic has 99% confidence level.

[0031] In step S120, the Z.sub.α value of the test statistic has a relationship of:

[00002]$Z_{\alpha }=\frac{\left|{\stackrel{\_}{r}}_{\mathrm{local}}-{\stackrel{\_}{r}}_{\mathrm{global}}\right|-d}{{\sigma }_{r,\mathrm{global}}/\sqrt{N_{\mathrm{local}}}};$

wherein r.sub.local is a local mean of coordinates, r.sub.global is a global mean of coordinates, σ.sub.r,global is a global standard deviation of coordinates, N.sub.local is the number of local sample events, and d is the predetermined bump tolerance. |r.sub.local−r.sub.global|≤d.

[0032] Accordingly, in the null hypothesis test, the null hypothesis states |r.sub.local−r.sub.global|, is small or equal to the predetermined bump tolerance. The steps of S120 to S140 then calculate and compare to ensure the statement is true or not as the LIDAR measured points have been converted to coordinates by the PCA technique. When the Z.sub.α value is greater than the Z score, the Z.sub.α value falls in the reject region, meaning that the null hypothesis statement is not true.

[0033] According to inventor's experimentation, using a Z-test of test statistics with converted coordinates, the results can be an indicator of local bumps.

[0034] In an embodiment, the predetermined bump tolerance is 1 centimeter, preferably within a range of 0.5 to 1.5 centimeters.

[0035] In actual practice, standardizing the target with a known bump size is used to determine the best value for bump tolerance and to minimize false negatives at the same confidence level. A grid size (where the grid is a region under analysis, for example, a 30 cm×30 cm area of a wall) may be optimized for minimal false positive rate (i.e., failing to detect bumps in a quality test.)

[0036] In one embodiment, calibrations for targets with different incident angles, ranges, texture and refractivity are performed to correct detection distortion before the surface flatness estimation.

EXAMPLE

Wall with a Bump/Projection

[0037] With reference to FIGS. 5 and 6A-6C, FIG. 5 is an exemplary diagram illustrating a LIDAR system being disposed to collect data points that represent a three-dimensional shape in a room; and FIGS. 6A-6C are exemplary diagrams illustrating the conversion of the LIDAR points' return to coordinates along the coordinate axes.

[0038] In this embodiment, as shown in FIG. 5, a LIDAR system is placed in an empty room and is configured to perform a 3D scanning that builds the 3D cloud point data of the room. However, it is noted that the ceiling and the floor are omitted for clarity, and the targets (i.e., the wall W1, W2, W3) are manually segmented. Each of the segmented walls are used as a target to test the performance of the Null hypothesis testing.

[0039] As above-mentioned, in step S110 of the present invention, a principal component analysis (PCA) is performed to transform the attributes of the target into coordinate axes. Since the assumption of the length and the width of the corresponding surface are much larger than the predetermined bump tolerance d, the length and width of the surface of the wall are aligned to PC1(x), PC2(y) axes respectively after PCA. PCA thus reduces the dimensionality of data such that a “one-dimensional” hypothesis test can be carried out in the direction of PC3(z) or “the thickness of the surface”.

[0040] As shown in FIGS. 6A-6C, PCA is performed to the segmented walls respectively that aligns the x-axis with the long side of the wall and z-axis with the thickness of the wall.

[0041] With further reference to FIGS. 7A-7B, 8A-8B and 9A-9B, FIGS. 7A and 7B are two-dimensional (2D) plot diagrams illustrating the distributions of the values by performing the method to the coordinates of FIG. 6A in accordance with an embodiment of the invention; FIGS. 8A and 8B are 2D plot diagrams illustrating the distributions of the values by performing the method to the coordinates of FIG. 6B in accordance with an embodiment of the invention; and FIGS. 9A and 9B are 2D plot diagrams illustrating the distributions of the values by performing the method to the coordinates of FIG. 6C in accordance with an embodiment of the invention.

[0042] As shown in FIG. 7A and 7B, the differences of the local mean of coordinates (r.sub.local) and global mean of coordinates (r.sub.global) of the first wall W1 are plotted in FIG. 7A. In FIG. 7A, the darkest region 700, near the middle bottom in the plot, indicates that the mean of the local coordinates and the global coordinates differ more than 1 cm and hence indicates a bump in the wall according to the predetermined bump tolerance of 1 cm. The Z.sub.a values of the first wall W1 are plotted in FIG. 7B. As shown in FIG. 7B, the region 710, near the middle bottom in the plot, indicates that the Za value is greater than the Z score (Z score is 1.645 at a confidence level of 95%, and color/gray scale is set to a range from 0 to 1.645) for a rejection of the null hypothesis. In other words, the mean of the local coordinates does deviate from the mean of the global coordinates of a value larger than the predetermined bump tolerance. This indicates that the region 710 failed the hypothesis test and a bump is “detected” on the first wall W1 near the middle bottom.

[0043] In similar manner, the differences of the local mean of coordinates (r.sub.local) and the global mean of coordinates (r.sub.global) of the second and third wall W2, W3 are plotted in FIGS. 8A and 9A, respectively. The Za values of the second and third wall W2, W3 are plotted in FIGS. 8B and 9B respectively. For walls W2 and W3, the measured point cloud is consistent with a flat surface within a predetermined bump tolerance of 1 cm. In other words, none of Za values plotted in FIGS. 8B and 9B is greater than Z score (1.645 at a confidence level of 95%).

[0044] The embodiments disclosed herein may be implemented using general purpose or specialized computing devices, mobile communication devices, computer processors, or electronic circuitries, including but not limited to digital signal processors (DSP), application specific integrated circuits (ASIC), field programmable gate arrays (FPGA), and other programmable logic devices configured or programmed according to the teachings of the present disclosure. Computer instructions or software codes running in the general purpose or specialized computing devices, mobile communication devices, computer processors or programmable logic devices can readily be prepared by practitioners skilled in the software or electronic art based on the teachings of the present disclosure.

[0045] In some embodiments, the present invention includes computer storage media having computer instructions or software codes stored therein, which can be used to program computers or microprocessors to perform any of the processes of the present invention. The storage media can include, but are not limited to, floppy disks, optical discs, Blu-ray Disc, DVD, CD-ROMs, and magneto-optical disks, ROMs, RAMs, flash memory devices, or any type of media devices suitable for storing instructions, codes and/or data.

[0046] The foregoing description of the present invention has been provided for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise forms disclosed. Many modifications and variations will be apparent to the practitioner skilled in the art.

[0047] The embodiments were chosen and described in order to best explain the principles of the invention and its practical application, thereby enabling others skilled in the art to understand the invention and its various embodiments and modifications. It is intended that the scope of the invention be defined by the following claims and their equivalence.