This document discusses using wavelet transformations to classify lunar terrain for autonomous spacecraft landings. It describes using a Gabor wavelet filter bank and circular Gabor wavelet on images of a simulated lunar landscape and region near Olympus Mons on Mars. The Gabor wavelet showed moderate success in interacting with textured areas, while the circular Gabor wavelet did not interact as well but was more computationally efficient. Edge detection was also tested and was successful at finding edges but unable to characterize near-edge regions. The goal is to use texture, edge, height and slope data to guide autonomous precision landing and obstacle avoidance.

1. Lunar Terrain Classification
Sean Brakken-Thal1,
Jacqueline LeMoigne-Stewart2 Autonomous Landing Experiment Wavelet Transformation
1:Washington Space Grant, University of Washington Wavelets are a family of functions that satisfy a set of certain mathematical properties. The
2:NASA Goddard Space Flight Center Code 580 wavelet transformation is a procedure of taking a prototype function called the mother wavelet
and creating a set of daughter wavelets. These daughter wavelets are scaled and translated copies
of the mother wavelet. By then convolving these daughter wavelets with the original signal a
Background set of wavelet coefficients are created for each part of the signal. This process of transforming a
signal into a set of wavelet coefficients is referred to as the wavelet transformation.
In 2004 NASA was given a new vision to return to exploration of the
The Gabor Wavelet has had past success in image processing for iris recognition and fingerprint
solar system. With the new vision they were given the challenge to re-
recognition but little research has been done on using the Gabor Wavelet for terrain classification.
turn to the moon by 2018 with the hope that a mission to Mars would Figure 6: HiRISE and Range Cameras
The Gabor wavelet is given by a harmonic function multiplied by a Gaussian function:
be possible as well. To accomplish the goal of returning to the Moon,
Currently missions to Mars and other objects in the solar system come at great risk due to the
NASA created the Constellation Program to design the new generation i2π x +ψ
x2 +γ 2 y 2
− 2σ2
inability to control the landers in real time. While NASA has the best landing procedures of any G=e λ e
of space craft. The program consists mainly of the development of the
other space administration much of the success of a landing comes down to luck. To increase
Ares Launch Vehicles, the Orion Crew Vehicle and the Altair Lunar
the reliability of landing it is suggested to place two cameras on a lander: A HiRISE camera for Instead of a complete expansion of the Gabor wavelet, a filter bank of several Gabor filters of
Lander. In addition to the development of the next generation of space
texture and edge detection and a LIDAR camera for height and slope detection. different dilation, orientation and phase is sufficient for terrain classification.
vehicles is the necessity to develop the next generation of data process-
Figure 1: Lunar Capsle
ing to aid in the ambitious goals to return to the solar system. This experiment tests the effectiveness of the two wavelets for texture classification in conjunc-
tion with edge detection, height classification and slope detection for a possible lunar terrain.
In data processing, image processing is one of the key areas under devel-
The experiment is to guide a landing craft by utilizing texture and edge
opment. Texture segmentation will aid the future of the NASA’s explo-
information from a HiRISE camera in conjunction to utilizing height
ration aspirations with applications in long-range, mid-range and short-
and slope information from a Range camera. The Range camera is used Figure 11: Gabor Filters
range planning. For long-range planning texture segmentation will help
to simulate a LIDAR camera.
in landing site selection and path selection. For mid-range and short- One Variation of the Gabor wavelet is the Circular Gabor wavelet. This wavelet differs from the
range planning texture segmentation has applications to autonomous To test the algorithms for landing and the different filters for the two traditional Gabor wavelet by being orientation invariant. Like the traditional Gabor wavelet it is
precision landing and obstacle avoidance. cameras a model of a possible lunar landscape was made. This model created by multiplying a sinusoid function with a Gaussian function:
ˆ
is then fixed to a platform that is able to move in the z direction while √
x2 +y 2 x2 +γ 2 y 2
Figure 2: Ares I − 2σ2
ˆ ˆ
the cameras are able to move in the x and y directions. By allowing the Figure 7: Lunar Model Gc = ei2π λ +ψ e
cameras to move in the horizontal directions while the platform moves
in the vertical a landing sequence is able to be tested. Shown below are some preliminary results
of the HiRISE camera using the Gabor filter, the Circular Gabor filter and an edge detector.
Figure 3: JSC
Figure 12: Gabor Filters
Texture Segmentation Olympus Mons Experiment
The process of breaking the image into regions of like characteristics is known as segmenta-
To test the effectiveness of the wavelet method a region of Martian terrain near Olympus Mons
tion. By segmenting the image into different regions further processing is able to be done to Figure 8: Gabor Filter Outputs of the Lunar Model (18◦N 133◦W ) was chosen to convolve with the Gabor and Circular Gabor filters. To simulate
classify a region based on its characteristics or to extract different features from the region.
The Gabor filter showed moderate success with it interacting with the expected areas of texture. how the filters would operate during a landing sequence several resolutions of the terrain near
Four filters were used to get the output shown which included two phases and two orientations. Olympus Mons were used. For the Gabor wavelet, 4 filters were used. For the Circular Gabor
One type of image segmentation is to break the image into different re- wavelet one filter was used.
gions based on the region’s texture. One of the underlying problems of
texture segmentation lies in how texture is defined. The phenomenon of
texture is one that is frequently experienced but differs so greatly given
the context of the experience that it is hard to define. One useful defini- Figure 4: Texture
tion is that a region of texture is a region of features, at some scale s0,
such that when the region is viewed from a larger scale, s1, the region becomes homogeneous. A
feature is a region, at some scales0, such that when viewed at a smaller scale, s1, the region be-
comes homogeneous. Thus by zooming out textures become homogeneous where as by zooming Figure 9: Circular Gabor Filter Output of the Lunar Model
in features become homogeneous. The Circular Gabor filter did not interact as well as the traditional Gabor filter though only one
A pixel of texture, then, would be one such that its neighborhood has a phase was tested. By only testing one phase the Circular Gabor filter took 25% of the computation Figure 13: Gabor Filter Outputs
large variance in the gray scale intensity of the image. Instead of calcu- time of the traditional Gabor Filter.
lating the variance of every pixel’s neighborhood it is more efficient to
convolve an image with a bank of filters that only interact strongly with
regions of texture. This process of filtering an image is called transform-
ing the signal. This is done in hopes that texture in the filtered image
Figure 5: Feature
will be easier to detect and thereby classify as “Good” or “Bad”.
Figure 10: Edge Detector Output of the Lunar Model
The edge detector was successful in finding the edges in the image. To be used for landing zone Figure 14: Gabor Filter Outputs
selection additional filters would be required due to its inability to interact with regions near an Figures 8 and 9 show a region near Olympus Mons, the Gabor and Circular Gabor filter outputs
edge. and the outputs after thresholding.