One of the simplest and commonly used image space approach to eliminate hidden surfaces is the Z-buffer or Depth Buffer algorithm. It is developed by Catmull. This algorithm compares surface depths at each pixel position on the on the projection plane. The surface depth is measured from the view plane along the z axis of a viewing system. When object description is converted to projection coordinates (x,y,z) each pixel position on the view plane is specified by x and y coordinate and z value gives the depth information. Thus object depths can be compared by comparing the z-values.
The Z-buffer algorithm is usually implemented in the normalized coordinates, so that z values range from at the back clipping plane to at the front clipping plane. The implementation requires another buffer memory called Z-buffer along with the frame buffer memory required for raster display devices. A Z-buffer is used to store depth values for each (x,y) position as surfaces are proceeds and the frame buffer stores the memory values for each position.
If the calculated depth values is greater than the value stored in the Z-buffer, the new depth value is stored, and the surfaced intensity at that position is determined and placed in the same xy location in the frame buffer
For Example, among three surfaces, surface $S_1$ has the smallest depth at view position (x,y) and hence highest z value. So it is visible at that position.
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