ISPRS Commission III, Vol.34, Part 3A „Photogrammetric Computer Vision“, Graz, 2002
STEREO PLANE MATCHING TECHNIQUE
Kazuo Oda, Takeshi Doihara, Ryosuke Shibasaki
Asia Air Survey Co., Ltd.
Atsugi-Shi, Kanagawa, Japan
Commission III
KEY WORDS: Stereo Matching, Surface Modeling, Projective Transformation, Homography
ABSTRACT:
This paper presents a new type of stereo matching algorithm called “Stereo Plane Matching”. Stereo plane matching adopts least
square method under the constraint that all points in an area specified by a polygon should lie on a common plane. This technique uti-
lizes the fact that correspondence between stereo images becomes 2-D projective transformation (homography) within an area where a
common plane is projected. Three corresponding point pairs on stereo image pair are used for parameterization of geometry of a plane,
which allows computation of homography within the polygon. The most powerful feature of this technique is that it can impose geo-
metrical constraint in planar direction or position. For example, the target plane can be fixed in horizontal or vertical direction, as well
as in other specified direction in 3-D space. Another feature is that it can be applied to unrectified stereo pair, so far as its orientation
parameters are known. Experimental results show that this algorithm can measure oblique roof or vertical wall of a building.
1. INTRODUCTION
Existing stereo matching techniques automatically measure
points or line features, but most of them cannot set constraint in
3-D shape of target objects, which includes one of the most sim-
ple 3-D structure, “Plane”. One approach of stereo matching
with planar constraint can be realized by image registration by
homography (Szeliski, 1994). This approach uses the fact that
correspondence between stereo images becomes 2-D projective
transformation (homography) within an area where a common
plane is projected. This approach can impose constraint on the
direction of planes parallel to specified plane (Oda et.al.,1997),
but other type of constraint, such as parallel to line direction, or
going through a specific point, cannot be attained.
In this paper, a new type of stereo matching algorithm called
“Stereo Plane Matching” is presented. Stereo plane matching
optimizes square difference of pixel value between stereo image
pair under constraint that all pixels in specified area should be on
a common plane. The most powerful feature of this technique is
that it can impose geometrical constraint in planar direction or
position. For example, a target plane can be fixed in horizontal
or vertical direction, as well as in other specified direction in 3-
D space. Another eminent feature is that stereo plane matching
can directly measure unrectified stereo pair under the condition
that its orientation parameters are known.
Stereo plane matching utilizes the fact that correspondence
between stereo images becomes 2-D projective transformation
(homography) within a region where a common plane is pro-
jected. Three corresponding point pairs, called “control pairs”,
parameterize the target plane geometry. It is a type of homogra-
phy with epipolar constraint, and computed by use of three con-
trol pairs and epipoles.
This paper first defines the target problem which stereo plane
matching technique handles, and presents the basic strategy of
stereo plane matching where an evaluation function for least
square method is formularized. The following sections show
details of stereo plane matching, including how to parameterize
a plane in stereo plane matching, how to derive homography
between stereo images, how to execute least square method and
how to impose constraint on plane position and direction. Some
experimental results are also presented to show that this method
can measure oblique roof and vertical wall in 3-D city space.
2. PROBLEM DEFINITION AND BASIC STRATEGY
2.1 Problem Definition
Suppose that object A consisted of planer faces is photographed
in image I, and I,, and polygon A in I, is measured as the
contour of face A of object A as show in Figure 1. The target
problem is how to determine three-dimensional coordinates of
polygon A automatically by stereo matching, under the con-
straint that all the points are co-planar, and the assumption that
interior and exterior orientation parameters of the stereo pair are
known. Interior and exterior orientation parameters can give the
following sets of coordinate transformation functions:
1) Transformation functions from 3D coordinates P(X, Y, Z)
to image coordinates p(x, y) which is projection of P :
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