EAST RUTHERFORD, N.J. (AP) For the New York Giants, one of the open competitions at training camp is at safety.

Last season's starters Antrel Rolle (Chicago Bears) and Stevie Brown (Houston Texans) left the Giants as free agents.

And so far the Giants don't have any clear-cut favorites to replace either Rolle at strong safety and Brown at free safety. Another veteran safety Quintin Demps was not re-signed.

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The lack of depth at the safety position has enabled veterans such as Cooper Taylor and Jeromy Miles to prove that they could be strong possibilities to start at either safety spot when the Giants open the season against the Dallas Cowboys on Sept. 13.

''I have to take advantage of every opportunity,'' said Taylor, who has spent two injury-filled seasons with the Giants after being selected in the fifth round in 2013.

''I definitely see this as a big chance for me and I think I have to step it up now, that my time has come. It's my year to prove myself here. I feel that I'm getting better every day. I think the competition is good for all of us. I'm just trying to do my best and see where I fit in.''

Taylor played 10 games, mostly on special teams, as a rookie in 2013 before ending up on the injured list with shoulder and hamstring problems. Last year he broke a bone in his foot in a preseason game against the Indianapolis Colts. He needed surgery and missed the season.

''I've dealt with the injuries and learned to overcome the adversity,'' said Taylor, who at 6-foot-4 and 228 pounds is the Giants' biggest defensive back.

''I changed my body composition a little and I've come back in better shape. I've had a full year to improve. I've been able to make plays and get my hands on the ball. I love that the position is wide open and I have to take advantage of this chance. I definitely feel like I have that edge.''

Miles spent his first four seasons with the Cincinnati Bengals and the past two with the Baltimore Ravens. He started two games last seasons with the Ravens and had 28 tackles with one interception and one forced fumble.

Although he's only 28, Miles is the oldest member of the Giants' safeties.

The Giants list three rookies (second-round pick Landon Collins out of LSU and fifth-round pick Mykkele Thompson out of Texas and undrafted Justin Currie out of UMass), two second-year players in Bennett Jackson and Nat Berhe, third-year player Taylor and fifth-year player Josh Gordy.

''I'm like the real old guy out there,'' Miles said. ''But I'm happy with the direction in which we're going back there. We have a great competition going on right now. We're going to see who the two best people are.

''Mentally, I have a good understanding of what is expected of me. If I can do something to wow people, then everything should be fine. ''

Both Taylor and Miles said that they're comfortable at either safety position.

''I've been playing both positions,'' Miles said. ''Whatever gives you the better opportunity to play, then I'm all for it. I'm here to compete. I don't focus too much on who's with the ones (the first unit) or the twos. I'm just trying to maximize the opportunity.''

The Giants traded up with the Titans to get the No. 33 pick overall to take Collins in the draft, but he has not been impressive in the early going of training camp.

Berhe, who was selected in the fifth round of last year's draft, was also expected to fill a spot at safety, but he's been sidelined with a calf injury. He's out indefinitely.

NOTES: Among the Giants who didn't practice Saturday were G Geoff Schwartz (foot), CB Prince Amukamara (groin), Berhe (calf), Jackson (quad) and LB Jameel McClain, who is still recovering from a stinger in his neck suffered Wednesday. ... WR Odell Beckham, Jr., the NFL Rookie of the Year last year, made two spectacular one-handed catches, causing Coughlin to say, ''Two hands please, two hands on the ball.'' ... Eli Manning threw his first two interceptions of the camp, one by CB Dominique Rodgers-Cromartie and the other by CB Trevin Wade. ... After taking Sunday off, the Giants will practice at their facility Monday, then head to Cincinnati for two practice sessions with the Bengals before opening the preseason next Friday night in Cincinnati.

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