"The AIT [scan] image cannot be saved, stored or shared, and the image automatically is deleted," said Villaraigosa.
"I have to take off my jacket," said L.A. City Councilwoman Janice Hahn. "Sometime I forget the blouse I'm wearing wasn't meant to be seen in public. But uh, you know what? These are small inconveniences, small embarrassments, in light of what we are trying to do."
A growing number of passengers are complaining of feeling violated and humiliated by the more invasive screening techniques by the Transportation Security Administration.
The full-body scanners can reveal a passenger's private area through their clothes, and those who refuse the scanner will have to undergo enhanced pat-downs.
Many travelers say the pat-downs are too invasive and cross the line of personal space.
A bladder cancer survivor from Michigan was patted down too roughly by a TSA agent in Detroit, and the bag he wears that collects his urine spilled onto his clothing. The retired special education teacher described the incident as humiliating to say the least, and he had to board the plane soaked in urine because he did not have time to change his clothes.
In another case, a breast cancer survivor was forced to reveal a prosthesis under the new stringent search procedure.
An online group is even organizing a boycott of full-body scans on Wednesday - calling it, National Opt-Out Day.
The Obama administration urged travelers not to participate in such boycotts as they could clog up security lines at airports around the nation on the busiest travel day of the year.
TSA rules state that passengers cannot opt out of both the scan and the pat-down once they have been selected for the enhanced searches. If they then try to evade the measures, they could face an $11,000 fine.
Even if someone in a security line becomes frustrated and decides not to fly, TSA rules require they submit to a scan or pat-down. If people were allowed to walk out, the agency says, would-be terrorists would have an easy escape.
The Associated Press contributed to this report.