If, at or prior to final confirmation of any special assessment, owners of more than fifty percent (50%) of the frontage of privately owned real property to be assessed for any improvement, or in the case of paving or similar improvements owners of more than fifty percent (50%) of the frontage to be assessed for any such improvement, shall object in writing to the proposed improvement, the improvement shall not be made by the proceedings authorized by this chapter without a four-fifth (4/5) vote of the members of the Council, provided that this section shall not apply to sidewalk construction.