Differential and integral invariants under image-perspective transformations: a report on work in progress

Eamon B. Barrett; Paul Max Payton; Michael H. Brill

doi:10.1117/12.23565

1 November 1990 Differential and integral invariants under image-perspective transformations: a report on work in progress

Eamon B. Barrett, Paul Max Payton, Michael H. Brill

Author Affiliations +

Proceedings Volume 1349, Applications of Digital Image Processing XIII; (1990) https://doi.org/10.1117/12.23565
Event: 34th Annual International Technical Symposium on Optical and Optoelectronic Applied Science and Engineering, 1990, San Diego, CA, United States

Abstract

The objective of this work is to develop automated techniques for recognizing the same objects in images that differ in scale tilt and rotation. Such perspective transformations of images are produced when aerial images of the same scene are taken from different vantage points. In previously reported work we have identified methods for deriving algebraic projective invariants under central projections. These methods generalize the familiar cross-ratio theorems for single images of finite sets of points on the line and in the plane. The algebraic methods do not utilize the intensity values of the images. Since image features essential for object recognition may be described in terms of derivatives and integrals of the image intensity it is necessary to investigate whether certain differential and integral operators applied to different perspective views of the same object are also invariant under the perspective transformation. We proceed to derive new differential operators and their corresponding integral invariants for curves and planar objects. Extensions to other image formation models such as synthetic aperture radar (SAR) are discussed. These results are steps toward a computational model for perspective-independent object recognition.

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Eamon B. Barrett, Paul Max Payton, and Michael H. Brill "Differential and integral invariants under image-perspective transformations: a report on work in progress", Proc. SPIE 1349, Applications of Digital Image Processing XIII, (1 November 1990); https://doi.org/10.1117/12.23565

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