We present a light-weight method for automatically detecting shapes that have an approximate rotational
symmetry (e.g., a square or equilateral triangle) on discrete-space images. Our motivation is the problem
of automatically detecting and recognizing hazardous material placards on a mobile platform (e.g., a mobile
telephone) equipped with a camera. The proposed method is
well-suited for mobile device applications,
which are characterized by limited memory, processing power and battery life. It is based on comparing the
magnitude of the coefficients of the Fourier series of the centralized moments of the Radon transform of the
image after segmentation. However, in our approach, the computation of the Radon transform is bypassed
as we obtain these coefficients directly from the rows of the Pascal Triangle of the segmented image. The
Pascal Triangle of an image is composed of complex moments arranged in a pyramidal fashion similar to
the binomial coefficients. These complex moments are obtained from a coarse segmentation of the shape
represented by a gray-scale image. In particular, the contours of the object do not need to be precisely
defined, and the shape needs not be connected. Moreover, our approach is invariant under translation,
rotation, and scaling. We tested our method on images from the
MPEG-7 shape database as well as images
from our own database of hazardous material placards.
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