I'm not an expert so i don't now exact reason but it's adviced on the internet to always use resistors with leds
In my opinion you should first think about the battery life. AA holds something like 2200mAh, AAA 850 mAh and 9V 270-500 mAh. If you connect two batteries in parallel your mAh will double and if in series your voltage will double(mAh stays the same).
Depending on your setup(ir filter, visible light filter etc.) your leds need 3 x 30-90mA = overall 90-270 mA. So you can calculate battery life easily... For example one AAA gives something like 850mAh so with two AAA's in series you get overall battery life of 850mAh / ( 3*70mA ) = 4 hours and voltage of 3V.
You can connect led in parallel or series. If parallel: voltage needed for 3 leds is 1.5V and if series 3x1.5V=4.5V. Basically you will have to think what kind of battery life you will need/want and how big batteries you want to install to your 3 point setup. Rechargeable batteries are an option but remember that the voltage is a bit smaller(1,2V per battery). When you have made a decision use that calcled to calculate proper resistors for your wanted mA per led.
Ps. I'm not really an expert on this but wanted to answer because this forum is quite dead. If someone notices an error please correct.
Pps. My model is in prototype-stage. I ended up using a separate 6V regulated power supply, 30mA current(ir filter removed and visible light filter installed). Prototype seemed to work fine now I just have to think the final design through and find the time and motivation to make the final version =)