LOS ANGELES — Construction cranes dot the sky from Century City to the Sunset Strip. Once-downtrodden blocks downtown and in Venice are bustling with restaurants, coffee shops, sparkling new condominiums, theaters and office construction. The unemployment rate has dropped to almost half its double-digit high of five years ago. Much of Los Angeles these days seems the portrait of prosperity.

But a sweeping census of the homeless population in Los Angeles County released last month came as a jolting rebuke to the charities and officials who have proclaimed a mission to end the region’s stubborn problem of people living on the streets. Their numbers spiked 12 percent in two years, cementing Los Angeles’s reputation of having the most intractable homeless problem in the nation. It is a place of unsettlingly stark class contrasts, on display every day with a staggering number of people living around the clock on the streets, without the extensive network of temporary overnight shelters provided in cities like New York City.

The report, by the Los Angeles Homeless Services Authority, has set off a wave of concern and frustration among officials here and raised questions about the widespread gentrification that has transformed parts of Los Angeles. The urban transformation, while bringing new life and prosperity to formerly bleak streets, has helped fuel some of the highest housing costs in the country, while removing inexpensive rentals from the market.

“It’s all being gentrified,” said Alice Callaghan, an advocate for the homeless, as she walked past people hidden under pieces of cardboard on Skid Row, an area in downtown Los Angeles. A few blocks away are stores like Big Man Bakes, with its promise of “fresh, moist, fantastic cupcakes” on a once bedraggled block of Main Street.