Thanks for your reply.
The C3088 camera module (with OV6620 image sensor) actually uses 5V for analog and 5/3.3V for digital. I am able to read other signals (such as HREF and VSYNC) from the module. Also, the module I have is an I2C module (the SCCB version of the sensor is probably old).
I used pull-up resistors for SDA, SCL (tried 10K and 4.7K; didn't work with either).
By the way, this module works fine for I2C with Arduino (device address = 0x60, speed = 100KHz).
I am going to try the software I2C tomorrow.