I have an esp8266 wifi module, arduino uno and an old mobile. I was wondering if there is any way by which i could remove the camera from the mobile and connect it with my arduino in order to view video captured by the camera. Is this possible by the hardware which i currently have? Or i will have to buy more hardware? Please let me know if more information is required also give the link of helpful articles.
Is there any way to connect my old phone camera with an arduino?
Yes, but it may be a huge amount of work requiring expensive equipment and skills that take decades to acquire.
See Mike's Electric - Interfacing a cheap phone camera module to a PIC32 microcontroller. which is a great video and will give you an idea of what is involved. Note that he's using a 32-bit microcontroller with relatively large RAM on the chip. You might need to use a 32-bit Arduino (Due etc) not one of the 8-bit Arduinos (Uno etc).
Mike is the kind of person who could reverse-engineer a random camera module from an old phone but this isn't a project for a typical Arduino user like you or I.
Since these camera modules cost about $1, it is probably best to look for a camera breakout for Arduino that comes with documentation and software libraries.
An Uno is undersized and underpowered (speed) for this job. Without even considering how to transfer the image, an Uno has nowhere for it to go. The most modest cell phone cameras' images were probably 3 Megapixels, and even assuming 2 bytes of storage per pixel (allowing 5 bits for each of 3 colors), you'd need 6 MB or 6000 KB to store the image. An Uno's RAM is 2K bytes before you subtract whatever RAM its program needs besides room to store the image. Based on those assumptions, an Uno would need another memory, 3000 times the size of its RAM, to hold the image.
Is there any possibility that the image is not stored in the arduino rather sent to the server in stream (i.e in small packets)?
I can't imagine why not - at least in theory - but I have no idea what kind of communication hardware might be built into the camera, or if you'd need to develop something on your own. But somehow you'll need to get the image data to the Arduino and in some kind of format you understand and can work with, at least once it gets to the web application. At this point, the critical piece of knowledge would be to know the specs of how the camera delivers image data - how fast, in what format, must the Arduino and the camera interact or does the data just pour out in a flood once started, ... ?
Your first steps will probably need to be to learn how some typical cameras handle this, and to figure out what specific camera you have and how that camera works. Then you'll have a much better idea about what it will take to complete your project.