WO2004099820A1

WO2004099820A1 - Method, system and storage medium concerning measurement of object structure

Info

Publication number: WO2004099820A1
Application number: PCT/SE2004/000685
Authority: WO
Inventors: Fredrik Andersson; Andreas Axelsson; Claes Johannesson; Kalle ÅSTRÖM
Original assignee: Airborne Hydrography AB
Current assignee: Airborne Hydrography AB
Priority date: 2003-05-06
Filing date: 2004-05-05
Publication date: 2004-11-18
Anticipated expiration: 2005-11-06
Also published as: SE0301308L; SE0301308D0; SE523650C2

Abstract

The invention concerns a method of determining the structure of an object by with the help of a transmitter which is arranged at a distance from the object transmit a series of pulses of electromagnetic radiation, wherein each pulse illuminates a portion of said object. With the helps of a receiver which is arranged at a distance from the object, the intensity of reflection pulses which are obtained by said transmitted pulses being reflected by the object is sensed. According to the invention, the variation in time of the intensity of a reflection pulse from the object is considered as a histogram over the distances to the different points within the portion of the object that has been illuminated by the transmitted pulse in question. The structure of the object is determined on the basis of a system of equations. The invention also concerns a system and a storage medium.

Description

Method, system and storage medium concerning measurement of object structure

TECHNICAL FIELD

The present invention concerns a method for determining the structure of an object, or the distance to different points on the object, by with the help of a transmitter which is arranged at a distance from the object transmitting a series of pulses of electromagnetic ra- diation, wherein each pulse illuminates a portion of said object. With the help of a receiver which is arranged at a distance from the object reflection pulses which are obtained by said transmitted pulses being reflected by the object are sensed. The measurement is done by observing the time it takes for a transmitted pulse to be reflected back from the object to the receiver. In particular, the invention intends to increase the resolution and the ro- bustness in laser measurements. The invention also concerns a system and a storage medium.

PRIOR ART

It is nowadays possible to with a receiver with time resolution register the intensity from the reflected light of a transmitted laser pulse. From the received intensity signal (wave form) the distance to the reflecting object is calculated as half the time difference times the speed of light between the transmission of the laser pulse and the reflection peak in the wave form.

It is nowadays possible to from an aeroplane or a helicopter carry out water depth measurements by using a laser bathymetric system. The system comprises a laser system, which emits pulsed radiation within the infrared wavelength range at t Q same time as it emits pulsed radiation within the wavelength range for visible light. The infrared radiation is reflected against the water surface while a considerable part of the visible light- penetrates the water and is reflected against the ground. The system also comprises a receiver with a detector arranged to register the intensity of the reflected, received radiation. A calculation unit connected to the detector calculates the time difference between the time when the radiation reflected at the water surface and the radiation reflected by the ground is received, wherein the water depth is calculated as half the time difference multiplied with the speed of light with compensation for the incident angle of the radiation against the water surface. In this manner information from one laser shot is used to determine one water depth.

Fig 1 exemplifies how the water depth determination can be carried out according to the prior art. Fig 1 thus shows an example of the detection of a detector of the reflection of a transmitted pulse. Fig 1 shows detected intensity as a function of time. The curve peak 10 originates from reflection at the water surface and the curve peak 12 originates from reflection at the ground. The time difference between t₂ and ti corresponds to the time it has taken for the light beam to go from the water surface to the ground and back to the water surface. On the basis of this time difference, the water depth can be calculated. t₂ and ti can be measured at for example the maximum value of the curve peaks, but it is also possible to measure on an inclined part of the curve peaks.

DESCRIPTION OF THE INVENTION

An object of the present invention is to improve the resolution at measurements of the kind which is indicated in the first paragraph above. In particular, the invention increases the resolution and the robustness in laser measurements by interpreting the reflection peak from each illumination as a histogram over the illuminated surface. Theories of histogram and its geometric moments are then used in order to set up a linear underdetermined system of equations where the depths are a linear function of the geometric moments. The underdetermined system of equations is then solved by minimising an error function comprising a regulative term. The method is particularly intended for laser bathymetric applications.

A further object is to increase the robustness at laser bathymetric measurements with the help of a laser. The object of the invention is achieved by a method according to claim 1. Different advantageous manners of carrying out the method according to the invention are clear from the claims 2-12. The object of the invention is also achieved by a system according to claim 13 and by a storage medium according to claim 14.

According to the prior art (see Fig 1) only the time difference t - ti has been considered. However, the shape of the intensity curve itself has not been considered. It has thus not made a difference for the evaluation whether the curve peak 12 is symmetrical or unsym- metrical. However, according to the present invention, the shape of the curve matters for the evaluation. As for example can be seen in Fig 1, the curve peak 12 is unsymmetrical. This makes a difference for the evaluation and leads to the fact that with the help of the calculation which will be described the resolution, among other things, is improved.

It should be noted that fundamental to the invention is the fact that when the light beam penetrates a medium (for example water) the light beam is scattered. It is thus not only one point at the ground which is hit by the light beam, but in fact a larger area. It is this area which is called "illuminated portion of the object" or "footprint" in the description below. The shape of the intensity peak 12 according to Fig 1 depends, inter alia, on how the depth varies within the area for a "footprint". According to the present invention, this will make a difference for the evaluation which leads to an improved result of the measurement. It should be noted that a better result of the measurement is obtained if the laser pulses are so close to each other that the different footprints partly overlap each other. However, it is not completely necessary for the invention that the footprints overlap each other.

The invention is primarily applicable for water depth measurement with the help of an aircraft. However, the invention is also applicable if the light pulses are transmitted from a measurement equipment (for example a boat) which is located at the water surface or under the water surface. In this case thus no peak corresponding to the peak 11 in Fig 1 is obtained. It is also conceivable to use the invention for topographic measurement, for example where an aeroplane flies over land and light pulses are reflected by the ground. It is should be noted that the expressions "light" and "illuminated portion" should not be interpreted as if the transmitted electromagnetic radiation must be within the visible wavelength range.

The advantages of the invention are achieved by considering the ground pulse as a histogram over the illuminated ground area and then use theories of histogram and its geometric moments for setting up a linear underdetermined system of equations with the unknown depths and calculating an optimal solution to this.

According to a possible manner of carrying out the method, the following is done:

- the whole ground pulse is extracted from the intensity signal for the reflected radiation

- the ground pulse is interpreted as a histogram over the depths which have been illuminated by the laser pulse

- a transformation matrix between the depths and the geometric moments is created with the help of the weight functions for each laser shot a linear underdetermined system of equations between the depths and the geometric moments is set up and an optimising solution is calculated.

The ground surface which is hit by laser light (footprint) can because of beam divergence and scattering phenomena have a diameter of between 1-10m depending on beam divergence, water quality and water depth. At closer shot distance than the diameter of the footprint there is overlapping information in the wave forms which is not used in conventional methods. When from each laser shot one depth is calculated, information from a large area is used to estimate the depth in the centre point. The information that the ground pulse contains concerning nearby depths is not used. By instead assuming that the ground pulse is a histogram over the depths which are illuminated, information from all illuminated positions on the ground can be used. The depths which are in the centre of the footprint will give a larger contribution to the histogram, since the highest light intensity is in the centre of the beam. With knowledge of the intensity distribution in the radiation that hits the ground, the weight functions can be estimated. The advantage with the invention is that it becomes possible to calculate the depths in a more dense resolution than the distance between each shot and that overlapping information is used to increase the robustness. It is in this manner possible to identify smaller objects and sharper ground contours, which is not possible when instead it is interpolated between the calculated depths. With a finer mapping of the ground it is also easier to position the centre of the shot at the correct position without having to round off too much. The calculated resolution can be increased or decreased depending on the purpose of the measurements. High resolution and small shot distances require a large amount of calculation time. Less resolution and larger shot distances give less possibility to identify small objects but can instead be carried out in real time.

Another advantage is that the information from a plurality of measurements at overlapping illumination is used to determine the depths.

SHORT DESCRIPTION OF THE DRAWINGS

Fig 1 shows schematically an example of sensed intensity as a function of time for a reflection pulse in accordance with the prior art.

Fig 2 shows schematically a similar curve as Fig 1 but where a histogram which is considered according to the present invention is indicated.

PREFERRED EMBODIMENTS

Fundamental to the invention is to consider the variation in time of the intensity of a reflection pulse from the object as a histogram over the distances to the different points within the portion of the object which has been illuminated by the transmitted pulse in question. Fig 2 illustrates schematically that the curve peak 12 can be considered as a histogram. On the basis of this, a system of equations can be set up. This is explained below. It should be noted that preferably the method is carried out automatically in that necessary steps are carried out by a computer on the basis of measurement data from the transmitter and the receiver. Let z(x_p,y_q) e D = {z_mm ,z_mn + dz, ,z_raax }be a discrete model of a ground structure, for example uniformly sampled in a square lattice. z(x_p,y_g) thus describes the depth at the point (Xp,y_g), where the integers j and q are indexes for the sampling points in the lattice, and furthermore that each depth is discrete with the smallest depth z_mm, largest depth z_max and with the resolution dz.

Each ground pulse from a laser shot can be seen as a weighted histogram over the depths which are within an area around the centre of the shot.

Mathematically such a histogram σ_(J (t ) for t e D can be described as

^σ> (0 = Σ ^h(^χ _P - ^χ,>y_q - yj \ = {(*_P ,y_q) - t = z(^χ _p , y_q )},

where h(x,y) is a weight function which describes the contribution at the position (x,y) relative to the centre of the laser shot, where the position of the centre is described by x, and y,.

The n:t geometric moment of a histogram σ_tJ(t) is defined as m„ (_W,) = ∑t"σ_;j (t). teD

The following relationship can be shown by changing the order of summation,

m„ (x, , y_} ) = ∑ (x_p - x_t,y_q - y_} )(z(x_p , y_q ))" .

P,1

The case when n = 1 is particularly interesting, since mι(x_hy) is a linear combination of the depths z. On the basis of this, a linear system of equations,

HZ = M, can be set up, where Z and M are column matrixes containing row stackings of z(x_p,y_q) and mι(Xj,y_j), respectively, and where the elements in H consist of the corresponding values for the weight functions. The explicit configuration of H depends on how the row stackings have been selected.

A common manner of solving overdetermined linear systems of equations is to minimise an error function V(Z) = (HZ - M)T(HZ-M) (least squares approximation). The system of equations above will however be underdetermined, but since we seek a fairly regular so- lution, we can create an overdetermined system by adding a regulative term. Let for ex- d² d² ample Δ_d be a discrete correspondence to the Laplace operator, Δ = — - + — - . The dx d regulative term then becomes Δ_dZ. If, furthermore, there is access to some approximate solution Zo, this can be taken into consideration by adding further term (Z-ZQ). Our error function then becomes

V(Z)=(HZ-M)^τ(HZ-M)+γ,(Δ_dZ)^τ(Δ_dZ)+γ₂(Z-Zo)^τ(Z-Zo),

where γj and γ₂ are weight constants. The error function is minimised by

Z = (H^TH+ _yι(Δ (Δ_d)+ γ₂I)-¹(A^τM+. γ₂Z₀),

which is thus an approximate solution .

In order to clarify, consider the following example with dz=l, z_mi„=0, z_max=10 (which gives D^~{0, 1, 2, 3 , 10}) and a discrete ground structure z(x_p,y_g) where q=l, 2, ..., 5 and p=l, 2, ..., 5 according to the below:

2 3 4 5 6

7 8 9 8 7 z(Xp > ,,) = 6 5 4 3 2 z(xι,yι) = 2, z(x₃,yι) = 9 etc.

3 4 5 6 7

8 9 8 7 6

For each (depth) t, A_t is thus the set of sampling points for which the depth z(x_p,y^ is equal to t and the laser measurement with the centre in (x y , σ"y(t), can thus be described by adding the weight functions over these.

Suppose that the configuration of the weight function is and otherwise zero.

This means: h(0, 0) = 3 h(-l,0) = l h(l, 0) = 1 h(0,-l) = 1 h(0 ,l) *= l. Histogram (1) as a function of the depth (t) then becomes as follows if the centre of measurement (1) is (i = 2,j = 2)

σ₂,2 (1) =

₂,₂ (3) = h (2-2,1-2) = h(0,-i = 2 σ₂,2 (4) - 0 σ_2/2 (5) = h (2-2,3-2) = h(0, 1) = 1 σ₂,₂ (6) - 0 σ_2f2 (7) = h (1-2,2-2) = h(-l,0) = 2 ₂,₂ (8) = h (2-2,2-2) = (0,0J = 3 σ_2r2 (9) = h (3-2,2-2) = h(i,o; - 2 σ_2ι2 (10) - 0

10 12

Depth in m

Histogram (2) as a function of the depth (t) then becomes as follows if the centre of measurement (2) is (i = 4,j = 4)

a_2l2 (0) = 0 σ₂,₂ (1) " 0 a ₂, 2 (2) = 0 σ_2l2 (3) = h(4-4,3-4) = h(0,-l) = 2 σ_2r2 (4) = 0 σ₂,₂ (5) = h (3-4,4-4) = h(-l,0) = 2 σ₂,₂ (6) = h(4-4,4-4) = fO,o = 3 σ₂,₂ (7) = h (5-4,4-4) + h (4-4,5-4) = (1 , 0) + h(0,l) = 1 + 1 = 2

σ_2r2 (9) = 0 σ₂,₂ (10) = 0

Depth in m

For the measurement (1) the first geometric moment becomes according to the following: mi (2, 2) = sum 3 + 5 + 7 + 24 + 9 = 48.

0 -σ_2r2(0) = 0

1 -02,2(1) = 1

3 -σ₂,₂(3) = 3

4 -σ_2ι2(4) = 4

5 -0₂,₂(5) = 5

6 -σ₂,₂(6) = 6

8 -σ₂,₂(8) = 8

9 -σ₂,₂(9) = 9

10 -σ₂,₂(10) = 10

For the measurement (2) the first geometric moment becomes according to the following: mι(4,4)^~ sum 3 + 5 + 18 + 14 = 40.

0 σ₄,₄(0) = 0 0 = 0

2 σ_t,,(2) = 2 0 = 0

3 σ₄,₄(3) = 3 1 = 3

4 σ₄,₄(4) = 4 0 = 0

5 σ₄,₄(5) = 5 1 = 5

6 σ_4/4(6) = 6 3 = 18

8 σ₄,₄(8) = 8 0 = 0

9 ₄,4(9) = 9 0 = 0

10 ^•σ₄,₄(10) = 1 0 0 = 0

If the row stacking has been selected such that z_!t z , ....,z₅ are given by x_p-l, y_q - 1, 2,

...,5 the system of equations HZ = M becomes explicitly:

0 1 0 0 0 1 3 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0^" 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 3 1 0 0 0 1 0

Claims

1. A method for determining the structure of an object, by a) with the help of a transmitter which is arranged at a distance from the object transmitting a series of pulses of electromagnetic radiation, wherein each pulse illuminates a portion of said object, b) with the help of a receiver which is arranged at a distance from the object sensing the intensity of reflection pulses which are obtained by said transmitted pulses be- ing reflected by the object, c) observing the time it takes for a transmitted pulse to be reflected back from the object to the receiver, d) considering the variation in time of the intensity of a reflection pulse from the object as a histogram over the distances to the different points within the portion of the object that has been illuminated by the transmitted pulse in question, e) repeating steps c) and d) for a plurality of reflection pulses, f) setting up a system of equations on the basis of the histograms which are based on the different reflection pulses, g) determining the structure of the object on the basis of the system of equations.

2. A method according to claim 1, wherein said system of equations is a linear under- determined system of equations which comprises geometric moments for said histogram and which has the distances to different points on the object as unknowns.

3. A method according to claim 1 or 2, wherein the structure of the object is determined in that a solution to the underdetermined system of equations is selected as the solution which minimises an error function V(f).

4. A method according to claim 3, wherein the error function V(f) which is minimised contains a regulative term.

5. ^• A method according to claim 3 or 4, wherein the error function Vφ which is minimised contains a first-estimation term.

6. A method according to any of the claims 3-5, wherein the error function Vφ which is minimised contains a regulative term γ₂(Bf)^τ(Bf) where γ₂ is a constant and the matrix B contains the second derivative for the distances or the depths

7. A method according to any of the claims 3-6, wherein the error function Vφ which is minimised contains a first-estimation term γι(f-fo) (f-fo) where γj is a constant and the vector fo contains an estimation of the unknown distances or depths/

8. A method according to any of the preceding claims, wherein said object is located under water.

9. A method according to claim 8, wherein said transmitter and receiver are located under water or at the water surface of the water volume in which the object is.

10. A method according to any of the claims 1-8, wherein said transmitter and receiver are not located under water and not at a water surface.

11. A method according to any of the preceding claims, wherein said transmitter transmits electromagnetic radiation produced with the help of a laser.

12. A method according to any of the preceding claims, wherein said transmitted series of pulses is transmitted such that the portions of said object which are illuminated by near by pulses partly overlap each other.

13. A system comprising a transmitter and a receiver of the kind used in the method according to any of the preceding claims and a computer arranged to automatically carry out the calculations which are described in any of the preceding claims.

14. A storage medium comprising a computer program which is such that when it is run on a computer as defined in claim 13 and when this computer is fed with data from a transmitter and a receiver concerning transmitted and sensed pulses, receptively, in accordance with any of the claims 1-12, the computer automatically carries out a calculation of the object structure in accordance with the method according to any of the claims 1-12.