Section 10. When the real estate of any person has been taken for the public use or has been damaged by the construction, maintenance, operation, alteration, repair or discontinuance of a public improvement or has been entered for a public purpose, but such taking, entry or damage was not effected by or in accordance with a formal vote or order of the board of officers of a body politic or corporate duly authorized by law, or when the personal property of any person has been damaged, seized, destroyed or used for a public purpose, and by such taking, damage, entry, seizure, destruction or use he has suffered an injury for which he is entitled to compensation, the damages therefor may be recovered under this chapter. If the injury was caused by or on behalf of the commonwealth or of a county, city, town or district, the officer or board of officers under whose direction or control the injury was caused shall award the damages upon the petition of any person entitled thereto. If the injury was caused by a railroad corporation, the county commissioners of the county in which the property taken, damaged, entered upon, seized, destroyed or used was located, and, if the injury was caused by a private corporation other than a railroad, the aldermen of the city or the selectmen of the town in which such property was located, shall award the damages upon the petition of any person entitled thereto or of the corporation liable therefor. In case of a specific taking, entry, seizure or other act causing destruction or damage or depriving the owner of the use of his property permanently or for a definite period of time the damages shall be assessed as of the date of such taking, entry, seizure or other act and the right thereto shall vest on such date and a petition for an award of damages therefor under this section may be filed within one year thereafter; otherwise damages shall be assessed with respect to any parcel of property as of the date when such property was first injuriously affected, the right thereto shall vest upon the completion of the public improvement which caused the injury, and a petition for an award of damages therefor under this section may be filed within one year after such completion.