Upon the petition in writing of persons owning the greater amount of frontage of property abutting upon any portion of a street, alley, public way or easement, or sewer right-of-way or easement, for any permanent improvement (which term is used in this section and the succeeding sections of this article to include any reimprovement) authorized in section one of this article, the governing body of any municipality may, after giving notice to abutting property owners as hereinafter in this article provided, by ordinance or resolution declare the necessity or convenience of such improvement and order and cause such portions of such streets, alleys, public ways or easements, or sewer right-of-ways or easements, to be graded, regraded, paved, repaved, surfaced, resurfaced, curbed, recurbed, sewered, resewered, permanently improved (which term is used in this section and the succeeding sections of this article to also mean reimproved) with sidewalks or otherwise permanently improved with suitable material, or any one or more of such improvements without the others, as may be determined by the governing body, to be made or constructed within such municipality or within such part or parts thereof as the governing body may determine, and such governing body may specially assess the entire cost of such improvements, or any part thereof, upon the property abutting on both sides of the portions of the streets, alleys, public ways or easements, or sewer right-of-ways or easements, improved.

The governing body of any municipality may also adopt such ordinance or resolution of necessity or convenience and provide for such improvements and the assessing of the cost thereof upon abutting property without such a petition of property owners having first been received, when the ordinance or resolution providing for such improvements is adopted by the affirmative vote of at least three fourths of the members of such governing body by recorded vote, after having given notice to abutting property owners as hereinafter in this article provided.