## 1aAO1. Estimating surface orientation from sonar images.

### Session: Monday Morning, May 13

### Time: 8:05

**Author: Nicholas C. Makris**

**Location: Naval Res. Lab., Washington, DC 20375**

**Abstract:**

Sonar images of remote surfaces are typically corrupted by signal-dependent
noise known as speckle. This noise arises when wavelength scale roughness on the
surface causes a random interference pattern in the sound field scattered from
it by an active system. Relative motion between source, surface, and receiver
cause the received field to fluctuate over time with complex Gaussian
statistics. Underlying these fluctuations, however, is the expected radiant
intensity from the surface, from which its orientation may be inferred. In many
cases of practical importance, Lambert's law is appropriate for such inference
because variations in the projected area of a surface patch, as a function of
source and receiver orientation, often cause the predominant variations in its
radiance. Therefore, maximum likelihood estimators for Lambertian surface
orientation are derived. These are asymptotically optimal when a sufficiently
large number of independent samples are available, even though the relationship
between surface orientation and measured radiance is generally nonlinear. Here,
the term optimal means that the estimate is unbiased and its mean square error
equals the Cramer--Rao lower bound, which is also derived. The requisite number
of independent samples necessary for asymptotic optimality of the maximum
likelihood estimate is given for some special cases.

from ASA 131st Meeting, Indianapolis, May 1996