Before proceeding with any improvement under section 17-509, the sufficiency of the protests or petitions or of the existence of the required facts and conditions shall be determined by the city council or village board of trustees at a hearing of which notice shall be given to all persons who may become liable for assessments by one publication in each of two successive weeks in a legal newspaper in or of general circulation in the city or village. Appeal from the action of the city council or village board of trustees may be made to the district court of the county in which the proposed district is situated. The sufficiency of the protests or petitions referred to in sections 17-510 and 17-511, as to the ownership of the property, shall be determined by the record in the office of the county clerk or register of deeds at the time of the adoption of such ordinance. In determining the sufficiency of the petitions or objections, intersections shall be disregarded, and any lot or ground owned by the city or village shall not be counted for or against such improvement.